Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#4699 |
| Sylow | C32 ⋊ #494 |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#67572, #11772023, C3×#67474, … |
| maximal normal subgroup of | C3×#67572, #11772023, C3×#67474, … |
| maximal quotient of | C3×#68063, C3×#68064, C3×#68065, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3678);