Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×Q8⋊(C67⋊C8) |
| Sylow | C67 ⋊ C2×Q8⋊C8 |
280 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×Q8⋊(C67⋊C8), Q8⋊C8×Dic67, #30746438, … |
| maximal normal subgroup of | C4×Q8⋊(C67⋊C8), Q8⋊C8×Dic67, #30746438, … |
| maximal quotient of | C2×#22558032, C2×#22558035, #30743778, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2887);