Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of Dic36 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×Dic36 |
| Sylow | C9 ⋊ C22×Q16 |
387 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | #11787471, #11787477, #11790989, … |
| maximal normal subgroup of | #11787471, #11787477, #11790989, … |
| maximal quotient of | C22×#63376, C22×#63378, C2×C4×Dic36, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1720);