Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C2×C83⋊C64 |
| unambiguous semidirect product | (C2×C83)⋊C64 |
| derived, Sylow | C83 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D83 |
| commutator, hypocenter | C83 | C2×C64 |
| Frattini | C32 | C2×D83 |
| Fitting | C2×C32×C83 | C2 |
| socle, prime radical | C22×C83 | C32 |
| cosocle | C32×C83 | C22 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C2×C32 | |
40 conjugacy classes of subgroups.
2752 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C64×Dic83, C4×C83⋊C64, #35292208, … |
| maximal normal subgroup of | C64×Dic83, C4×C83⋊C64, #35292208, … |
| maximal quotient of | C4×C83⋊C64, C22⋊(C83⋊C64), C4⋊(C83⋊C64), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2719);