Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #63626 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×#63627 |
| Fitting | C2×C32×C16 ⋊ C2 |
| Sylow | C32 ⋊ C2×SD32 |
270 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #11797655, C4×#63627, #11797688, … |
| maximal normal subgroup of | #11797655, C4×#63627, #11797688, … |
| maximal quotient of | C2×#10589375, C2×#10589369, C2×#10589371, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4484);