Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C22×C3×#235 |
| Fitting | C23×C32×C4 ⋊ C2 |
| Sylow | C32 ⋊ C22×#41 |
1898 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#69956, #11784587, C3×#69537, … |
| maximal normal subgroup of | C3×#69956, #11784587, C3×#69537, … |
| maximal quotient of | C22×C3×#872, C22×C3×#926, C22×C3×C4×#67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8608);