Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#5403 |
125 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #11920599, #11920600, #11920605, … |
| maximal normal subgroup of | #11920599, #11920600, #11920605, … |
| maximal quotient of | C3×#73013, C3×#73015, C3×#73011, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5471);