Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | Dic3×#237 |
| Sylow | C32 ⋊ C4×#41 |
667 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #11859985, #11859987, Dic3×#912, … |
| maximal normal subgroup of | #11859985, #11859987, Dic3×#912, … |
| maximal quotient of | Dic3×#877, Dic3×#892, Dic3×#67⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7068);