Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×Dic3×#67 |
| Sylow | C32 ⋊ C2×C4×D4 |
918 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#806, #11785095, C4×Dic3×#67, … |
| maximal normal subgroup of | Dic3×#806, #11785095, C4×Dic3×#67, … |
| maximal quotient of | C2×Dic3×(C2×D3)⋊C4, C2×Dic3×#217, C2×Dic3×Dic3⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7379);