Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#5514 |
| Fitting | C2×C32×C4⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ #553 |
522 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#78760, C3×#81485, #11887406, … |
| maximal normal subgroup of | C3×#78760, C3×#81485, #11887406, … |
| maximal quotient of | C3×#82160, C3×#73634, C3×#82161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7493);