Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #576×D83 |
| Fitting | #576×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#576 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D4×D83 |
| commutator, cosocle | C4×C83 | C25 |
| Frattini | C4 | C24×D83 |
| Fitting | #576×C83 | C2 |
| socle | C2×C83 | C23×D4 |
| hypercenter | #576 | D83 |
| hypocenter | C83 | C2×#576 |
| LCS | G ▷ C4×C83 ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #576 | |
1512 conjugacy classes of subgroups.
946 conjugacy classes — view the full character table.
| maximal subgroup of | #2192×D83, #2194×D83, #35558366, … |
| maximal normal subgroup of | #2192×D83, #2194×D83, #35558366, … |
| maximal quotient of | #2897×D83, #2913×D83, #2946×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19258);