Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C3×#926 |
| Sylow | C32 ⋊ C2×#117 |
778 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#71965, C3×#71980, #11783115, … |
| maximal normal subgroup of | C3×#71965, C3×#71980, #11783115, … |
| maximal quotient of | C2×C3×#4932, C2×C3×C4×#217, C2×C3×C4×C4⋊Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7765);