Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #63653 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×#63656 |
| Sylow | C32 ⋊ C2×Q32 |
246 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | #11797694, C4×#63656, #11797714, … |
| maximal normal subgroup of | #11797694, C4×#63656, #11797714, … |
| maximal quotient of | C2×#10589358, C2×#10589430, C2×#10589355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4761);