Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×Q16×D67 |
| Fitting | C4×Q16×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×C4×Q16 |
488 conjugacy classes of subgroups.
980 conjugacy classes — view the full character table.
| maximal subgroup of | #1332×D67, #30765582, #1334×D67, … |
| maximal normal subgroup of | #1332×D67, #30765582, #1334×D67, … |
| maximal quotient of | C8×Q16×D67, #1584×D67, #1591×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13271);