Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C22×C67⋊C32 |
| derived, Sylow | C67 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | D67 |
| commutator, hypocenter | C67 | C22×C32 |
| Frattini | C16 | C22×D67 |
| Fitting | C22×C16×C67 | C2 |
| socle | C23×C67 | C16 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C22×C16 | |
120 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30743517, #30743518, #30743529, … |
| maximal normal subgroup of | #30743517, #30743518, #30743529, … |
| maximal quotient of | C2×C4×C67⋊C32, C2×C22⋊(C67⋊C32), C2×C4⋊(C67⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6799);