Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C2×A4×D12 |
| unambiguous semidirect product | (C23×D12)⋊C3 |
| Fitting | C23×C3×C4 ⋊ C2×C3 |
650 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #11920648, #11920649, #11920650, … |
| maximal normal subgroup of | #11920648, #11920649, #11920650, … |
| maximal quotient of | A4×#869, C4×A4×D12, A4×#874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8491);