Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C24×C83⋊C8 |
| derived, Sylow | C83 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | D83 |
| commutator, hypocenter | C83 | C24×C8 |
| Frattini | C4 | C24×D83 |
| Fitting | C24×C4×C83 | C2 |
| socle, prime radical | C25×C83 | C4 |
| cosocle | C4×C83 | C25 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C24×C4 | |
1976 conjugacy classes of subgroups.
2752 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35309627, #35309629, #35309653, … |
| maximal normal subgroup of | #35309627, #35309629, #35309653, … |
| maximal quotient of | C23×C4×C83⋊C8, C23×C22⋊(C83⋊C8), C23×C4⋊(C83⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19209);