Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | #408×D67 |
| Fitting | #408×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#408 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D67 |
| commutator, socle | C22×C67 | C23×C4 |
| Fitting | #408×C67 | C2 |
| hypercenter | #408 | D67 |
| hypocenter | C67 | C2×#408 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C4 ◁ #408 | |
792 conjugacy classes of subgroups.
980 conjugacy classes — view the full character table.
| maximal subgroup of | #1315×D67, #30764901, #30764904, … |
| maximal normal subgroup of | #1315×D67, #30764901, #30764904, … |
| maximal quotient of | #1468×D67, #1469×D67, #1470×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 12947);