Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#5770 |
| Fitting | C32×#135 ⋊ C2 |
| Sylow | C32 ⋊ #577 |
547 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#84009, C3×#79900, #11886604, … |
| maximal normal subgroup of | C3×#84009, C3×#79900, #11886604, … |
| maximal quotient of | C3×#78831, C3×#78832, C3×#79178, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7749);