Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #64214 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊AGL(1,𝔽9) |
| Fitting | C2×C32×C4 ⋊ C8 |
| Sylow | C32 ⋊ C2×C4⋊C8 |
165 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | #11770756, #11770796, #11770866, … |
| maximal normal subgroup of | #11770756, #11770796, #11770866, … |
| maximal quotient of | C2×#10593252, C2×#10593253, #11776820, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8365);