Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D32×D83 |
| Fitting | D32×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×D32 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D16×D83 |
| commutator, cosocle | C16×C83 | C23 |
| Frattini | C16 | C22×D83 |
| Fitting | D32×C83 | C2 |
| socle | C2×C83 | C2×D16 |
| hypercenter | D32 | D83 |
| hypocenter | C83 | C2×D32 |
| LCS | G ▷ C16×C83 ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D32 | |
120 conjugacy classes of subgroups.
817 conjugacy classes — view the full character table.
| maximal subgroup of | D64×D83, SD128×D83, #35325460, … |
| maximal normal subgroup of | D64×D83, SD128×D83, #35325460, … |
| maximal quotient of | #1415×D83, #1423×D83, #35324975, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6806);