Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#16863514 |
| Fitting | C2×C4×C8×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#443 |
472 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#22558181, C2×#22558183, #30765617, … |
| maximal normal subgroup of | C2×#22558181, C2×#22558183, #30765617, … |
| maximal quotient of | C2×C8×D536, C2×C8×#11761617, C2×C8×Dic268, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13401);