Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #137×Dic67 |
| Sylow | C67 ⋊ C4×#137 |
484 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
| maximal subgroup of | #455×Dic67, #30861719, #456×Dic67, … |
| maximal normal subgroup of | #455×Dic67, #30861719, #456×Dic67, … |
| maximal quotient of | #137×C67⋊C8, #30825427, #30825450, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13331);