Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#5579 |
| Fitting | C32×C4×Q8 ⋊ C2 |
| Sylow | C32 ⋊ #554 |
491 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#71028, C3×#68244, #11779025, … |
| maximal normal subgroup of | C3×#71028, C3×#68244, #11779025, … |
| maximal quotient of | C3×#73768, C3×C4⋊C4×D12, C3×#73770, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7558);