Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#5507 |
| Fitting | C2×C32×C4⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ #547 |
630 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#78757, C3×#81302, #11887012, … |
| maximal normal subgroup of | C3×#78757, C3×#81302, #11887012, … |
| maximal quotient of | C3×#73368, C3×#73767, C3×#82159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7486);