Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #64214 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#64218 |
| Sylow | C32 ⋊ C2×M32 |
117 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | #11772316, #11772337, #11772433, … |
| maximal normal subgroup of | #11772316, #11772337, #11772433, … |
| maximal quotient of | C2×#10593263, C4×#64218, C2×C22⋊#3771, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8372);