Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #578×D83 |
| Fitting | #578×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#578 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D4×D83 |
| commutator, cosocle | C4×C83 | C25 |
| Frattini | C4 | C24×D83 |
| Fitting | #578×C83 | C2 |
| socle | C2×C83 | C23×D4 |
| hypercenter | #578 | D83 |
| hypocenter | C83 | C2×#578 |
| LCS | G ▷ C4×C83 ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #578 | |
1408 conjugacy classes of subgroups.
946 conjugacy classes — view the full character table.
| maximal subgroup of | #2193×D83, #2195×D83, #35558375, … |
| maximal normal subgroup of | #2193×D83, #2195×D83, #35558375, … |
| maximal quotient of | #2898×D83, #2913×D83, #2947×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19272);