Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #3788 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×#63765 |
| Sylow | C32 ⋊ C2×M32 |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #11772279, #11772304, #11772319, … |
| maximal normal subgroup of | #11772279, #11772304, #11772319, … |
| maximal quotient of | C2×#10590175, C4×#63765, C2×#10590176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5643);