Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #554×D83 |
| Fitting | #554×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#554 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D83 |
| commutator, socle, cosocle | C22×C83 | C25 |
| Fitting | #554×C83 | C2 |
| prime radical | C2×D4×D83 | C22 |
| hypercenter | #554 | D83 |
| hypocenter | C83 | C2×#554 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ #554 | |
1200 conjugacy classes of subgroups.
1075 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1622×D83, #1632×D83, #1643×D83, … |
| maximal normal subgroup of | #1622×D83, #1632×D83, #1643×D83, … |
| maximal quotient of | #2345×D83, D4×C4⋊C4×D83, #2349×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 18037);