Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×#64133 |
| Sylow | C32 ⋊ C2×C22⋊Q8 |
966 conjugacy classes of subgroups; only the 327 normal subgroups are shown.
This group has 966 conjugacy classes of subgroups — too many to draw. Only its 327 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | #11774102, #11774108, #11774118, … |
| maximal normal subgroup of | #11774102, #11774108, #11774118, … |
| maximal quotient of | C2×#10592911, C2×#10592909, C2×#10592632, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8137);