Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×Q16×Dic67 |
| Sylow | C67 ⋊ C2×C4×Q16 |
488 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 245 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
980 conjugacy classes — view the full character table.
| maximal subgroup of | #358×Dic67, #30771052, #362×Dic67, … |
| maximal normal subgroup of | #358×Dic67, #30771052, #362×Dic67, … |
| maximal quotient of | C2×Q16×C67⋊C8, C2×#22559060, C2×#22559106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13275);