Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#4689 |
| Fitting | C32×C4×C8 ⋊ C2 |
| Sylow | C32 ⋊ #405 |
282 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#69051, C3×#69072, #11795894, … |
| maximal normal subgroup of | C3×#69051, C3×#69072, #11795894, … |
| maximal quotient of | C3×C8×ΓL(1,𝔽25), C3×#68047, C3×#68070, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3668);