Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×#126×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2723 |
498 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,b^2=ef,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35611833, #35611846, #35611950, … |
| maximal normal subgroup of | #35611833, #35611846, #35611950, … |
| maximal quotient of | #35331965, #35332129, #35332144, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 11425);