Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | #386×D67 |
| Fitting | #386×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#386 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D67 |
| commutator | C22×C67 | C23×C4 |
| Fitting | #386×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | #386 | D67 |
| hypocenter | C67 | C2×#386 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #386 | |
1576 conjugacy classes of subgroups.
980 conjugacy classes — view the full character table.
| maximal subgroup of | #1390×D67, #30772068, #1790×D67, … |
| maximal normal subgroup of | #1390×D67, #30772068, #1790×D67, … |
| maximal quotient of | C22⋊#95×D67, #1436×D67, #1437×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6924);