Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×C3×C3⋊#95 |
| unambiguous semidirect product | (C2×C3)⋊(C3×#95) |
| Sylow | C32 ⋊ C2×#95 |
778 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#67674, #11770811, C3×#67624, … |
| maximal normal subgroup of | C3×#67674, #11770811, C3×#67624, … |
| maximal quotient of | C3×C4×C3⋊#95, C3×#71544, C3×#72127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4187);