Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #544×D83 |
| Fitting | #544×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#544 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D83 |
| commutator, socle, cosocle | C22×C83 | C25 |
| Fitting | #544×C83 | C2 |
| prime radical | C23×D83 | C23 |
| hypercenter | #544 | D83 |
| hypocenter | C83 | C2×#544 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ #544 | |
1080 conjugacy classes of subgroups.
946 conjugacy classes — view the full character table.
| maximal subgroup of | #1599×D83, #1605×D83, #1611×D83, … |
| maximal normal subgroup of | #1599×D83, #1605×D83, #1611×D83, … |
| maximal quotient of | #2316×D83, #2317×D83, #2329×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17906);