Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×#16863164 |
| Sylow | C67 ⋊ C2×#343 |
432 conjugacy classes of subgroups.
1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #343×Dic67, C4×#16863164, #30761097, … |
| maximal normal subgroup of | #343×Dic67, C4×#16863164, #30761097, … |
| maximal quotient of | C2×#22558051, #30745427, #30745430, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4245);