Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#5561 |
| Fitting | C32×C4×D4 ⋊ C2 |
| Sylow | C32 ⋊ #542 |
479 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#79594, C3×#79886, #11872155, … |
| maximal normal subgroup of | C3×#79594, C3×#79886, #11872155, … |
| maximal quotient of | C3×#73760, C3×#82325, C3×#73625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7540);