Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #4519 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#4520 |
| Sylow | C32 ⋊ SD64 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×SD64, C2×C3×#4520, D3×#4520, … |
| maximal normal subgroup of | C3×D3×SD64, C2×C3×#4520, D3×#4520, … |
| maximal quotient of | C3×#67824, C3×#67578, C3×#67576, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1146);