Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#99×D67 |
| Fitting | C2×#99×C67 ⋊ C2 |
| Sylow | C67 ⋊ C22×#99 |
1112 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
| maximal subgroup of | #1390×D67, #30770776, #1393×D67, … |
| maximal normal subgroup of | #1390×D67, #30770776, #1393×D67, … |
| maximal quotient of | C2×#323×D67, C2×#324×D67, #1459×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 12961);