Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#5651 |
| Sylow | C32 ⋊ #563 |
431 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#71003, C3×#69141, #11798721, … |
| maximal normal subgroup of | C3×#71003, C3×#69141, #11798721, … |
| maximal quotient of | C3×#74682, C3×#82840, C3×#75492, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7630);