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 | C3×C8×#67 |
| Fitting | C22×C32×C8 ⋊ C2 |
| Sylow | C32 ⋊ C8×D4 |
306 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#67⋊C16, C3×C16×#67, #67×C3⋊C16, … |
| maximal normal subgroup of | C3×#67⋊C16, C3×C16×#67, #67×C3⋊C16, … |
| maximal quotient of | C3×C8×#213, C3×C8×#214, C3×C8×#215, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4088);