Order = 17971200 =
211.33.52.13.
Mult = 1.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of 2F4(2)' = T are a, b where a is in class 2A, b has order 3 and ab has order 13.
Standard generators of 2F4(2)'.2 = 2F4(2) are c, d where c is in class 2A, d is in class 4F, cd has order 12 and cdcd2cd3 has order 4.
Presentations
| Group | Presentation | Link |
|---|---|---|
| 2F4(2)' | 〈 a, b | a2 = b3 = (ab)13 = [a, b]5 = [a, bab]4 = ((ab)4ab−1)6 = 1 〉 | Details |
| 2F4(2)'.2 | 〈 c, d | c2 = d4 = (cd)12 = (cd2)8 = [c, d]5 = (cdcd2cd3)4 = (cdcd2cd2cd2)3cd−1(cd2)3 = [c, (dc)3(d−1c)2dcd−1cd−2] = [c, dcdcd−1cd2]2 = [c, d2cd]4 = (cd)4cd2cd(cd−1)4cd(cd2cd−1)2cdcd2cdcdcd−1cd−1cdcd2 = 1 〉 | Details |
Representations
Representations of 2F4(2)'
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 1600 Std Details 1755 Std Details 2304 Std Details 2925 Std Details 12480 Std Details 14976 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 C 26 a Std Details 0 C 26 b Std Details 0 Q(i) 27 a Std Details 0 Q(i) 27 b Std Details 0 Z 52 Std Details 0 Z 78 Std Details Char Ring Dimension ID Generators Description Link 2 GF(2) 26 Std Details 2 GF(2) 246 Std Details 2 GF(4) 2048 a Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 26 a Std Details 3 GF(3) 26 b Std Details 3 GF(9) 27 a Std Details 3 GF(9) 27 b Std Details 3 GF(3) 54 Std Details 3 GF(3) 77 Std Details 3 GF(3) 124 a Std Details 3 GF(3) 124 b Std Details Char Ring Dimension ID Generators Description Link 5 GF(25) 26 a Std Details 5 GF(25) 26 b Std Details 5 GF(5) 27 a Std Details 5 GF(5) 27 b Std Details 5 GF(5) 52 Std Details 5 GF(5) 78 Std Details 5 GF(25) 109 a Std Details 5 GF(25) 109 b Std Details 5 GF(5) 218 Std Details Char Ring Dimension ID Generators Description Link 13 GF(169) 26 Std Details 13 GF(13) 27 a Std Details 13 GF(13) 27 b Std Details 13 GF(13) 52 Std Details 13 GF(13) 78 Std Details
Representations of 2F4(2)'.2
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 1755 Std Details 2304 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 26 Std Details 2 GF(2) 246 Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 52 Std Details 3 GF(3) 54 Std Details 3 GF(3) 77 Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 27 Std Details 5 GF(5) 52 Std Details 5 GF(5) 78 Std Details 5 GF(5) 218 Std Details Char Ring Dimension ID Generators Description Link 13 GF(13) 27 a Std Details 13 GF(13) 27 b Std Details 13 GF(13) 78 Std Details 13 GF(13) 1374 Std Details
Maximal subgroups
Maximal subgroups of 2F4(2)'
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| L3(3):2 | Program: Generators |
||
| L3(3):2 | Program: Generators |
||
| 2.[28].5.4 | Program: Generators |
||
| L2(25) | Program: Generators |
||
| 22.[28].S3 | Program: Generators |
||
| A6.22 | Program: Generators |
||
| A6.22 | Program: Generators |
||
| 52:4A4 | Program: Generators |
Maximal subgroups of 2F4(2)'.2
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| 2F4(2)' | Program: Standard
generators |
||
| 13:12 = F156 | |||
| 31+2:SD16 | |||
| 2.[29].5.4 | |||
| L2(25).23 | |||
| 22.[29].S3 | |||
| 52:4S4 |
Conjugacy classes
Conjugacy classes of 2F4(2)'
| Conjugacy class | Centraliser order | Power up | Class rep(s) |
|---|---|---|---|
| 1A | 17 971 200 |
Omitted
owing to
length. |
|
| 2A | 10 240 |
Omitted
owing to
length. |
|
| 2B | 1 536 |
abababbababababbababababbababababbab |
|
| 3A | 108 |
abababbabababbabababbabababb |
|
| 4A | 192 |
(abababb)3 |
|
| 4B | 128 |
Omitted
owing to
length. |
|
| 4C | 64 |
abababbababababbab |
|
| 5A | 50 |
aabababbababababbabaabababbababababbab |
|
| 6A | 12 |
abababbabababb |
|
| 8A | 32 |
Omitted
owing to
length. |
|
| 8B | 32 |
Omitted
owing to
length. |
|
| 8C | 16 |
abababbab |
|
| 8D | 16 |
aabababbababababbabaabababbab |
|
| 10A | 10 |
aabababbababababbab |
|
| 12A | 12 |
abababb |
|
| 12B | 12 |
(abababb)5 |
|
| 13A | 13 | ab |
|
| 13B | 13 |
abab |
|
| 16A | 16 |
(abbaabababbababababbabaabababbab)5 |
|
| 16B | 16 |
(abbaabababbababababbabaabababbab)3 |
|
| 16C | 16 |
abbaabababbababababbabaabababbab |
|
| 16D | 16 |
(abbaabababbababababbabaabababbab)15 |
Download words for class representatives.