Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#63357 |
| Fitting | C2×C9×C16 ⋊ C2 |
| Sylow | C9 ⋊ C2×M32 |
135 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #11772698, C4×#63357, #11795849, … |
| maximal normal subgroup of | #11772698, C4×#63357, #11795849, … |
| maximal quotient of | C2×#10588179, C4×#63357, C2×(C2×D9)⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 462);