Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×Dic3⋊C8 |
| Sylow | C32 ⋊ C2×C4⋊C8 |
314 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#67524, #11771442, C3×#68602, … |
| maximal normal subgroup of | C3×#67524, #11771442, C3×#68602, … |
| maximal quotient of | C2×C3×#4480, C2×C3×#4479, C3×#70745, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4078);