Order = 23499295948800 = 220.35.52.7.17.31.
Mult = 1.
Out = 2.

Porting notes

Porting incomplete.

Standard generators

Standard generators of O10+(2) are a, b where a is in class 2A, b is in class 20A and ab has order 21.

Standard generators of O10+(2):2 are c, d where c is in class 2E, d has order 16 and cd has order 45.

Presentations

Group Presentation Link
O10+(2):2 〈 c, d | c2 = d16 = (cd)45 = [c,d]3 = [c,d2]2 = [c,d3]3 = [c,d4]2 = [c,d5]2 = [c,d6]2 = [c,d7]2 = (cd8)4 = (cd2cd2cd−1)9 = 1 〉 Details

Representations

Representations of O10+(2)

Representations of O10+(2):2

Maximal subgroups

Maximal subgroups of O10+(2)

Subgroup Order Index Programs/reps
S8(2) Program: Generators
28:O8+(2) Program: Generators
210:L5(2) Program: Generators
210:L5(2) Program: Generators
(3 × O8-(2)):2
21+12:(S3 × A8)
23+12:(S3 × S3 × L3(2))
(A5 × U4(2)):2
(S3 × S3 × A8):2

Maximal subgroups of O10+(2):2

Subgroup Order Index Programs/reps
O10+(2)
S8(2) × 2
28:O8+(2):2
S3 × O8-(2):2
21+12:(S3 × S8)
[215]:A8
23+12:(32:D8 × L3(2))
L5(2):2
S5 × U4(2):2
(S3 × S3):2 × S8