Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #564×D83 |
| Fitting | #564×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#564 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D83 |
| commutator, socle, cosocle | C22×C83 | C25 |
| Fitting | #564×C83 | C2 |
| prime radical | C22×D83 | C24 |
| hypercenter | #564 | D83 |
| hypocenter | C83 | C2×#564 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ #564 | |
896 conjugacy classes of subgroups.
817 conjugacy classes — view the full character table.
| maximal subgroup of | #1658×D83, #1663×D83, #35385704, … |
| maximal normal subgroup of | #1658×D83, #1663×D83, #35385704, … |
| maximal quotient of | #2382×D83, #35567124, #564×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 18652);