Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C23 |
| direct product | C3×#4550 |
| Sylow | C32 ⋊ #336 |
274 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#336, C2×C3×#4550, D3×#4550, … |
| maximal normal subgroup of | C3×D3×#336, C2×C3×#4550, D3×#4550, … |
| maximal quotient of | C3×C3⋊#1273, C3×#67737, C3×#67740, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1176);