Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C22×C83⋊C32 |
| derived, Sylow | C83 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | D83 |
| commutator, hypocenter | C83 | C22×C32 |
| Frattini | C16 | C22×D83 |
| Fitting | C22×C16×C83 | C2 |
| socle, prime radical | C23×C83 | C16 |
| cosocle | C16×C83 | C23 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C22×C16 | |
120 conjugacy classes of subgroups.
2752 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35292090, #35292091, #35292102, … |
| maximal normal subgroup of | #35292090, #35292091, #35292102, … |
| maximal quotient of | C2×C4×C83⋊C32, C2×C22⋊(C83⋊C32), C2×C4⋊(C83⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6799);