Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×D664 |
| Fitting | C23×C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C23×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D332 |
| commutator, cosocle | C4×C83 | C25 |
| Frattini | C4 | C24×D83 |
| Fitting | C23×C8×C83 | C2 |
| socle | C24×C83 | D4 |
| hypercenter | C23×C8 | D83 |
| hypocenter | C83 | C23×D8 |
| LCS | G ▷ C4×C83 ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
1976 conjugacy classes of subgroups.
2680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35311202, #35311204, #35311228, … |
| maximal normal subgroup of | #35311202, #35311204, #35311228, … |
| maximal quotient of | C23×#14581714, C23×#14581726, C22×C4×D664, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19226);