Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#5118 |
| Sylow | C32 ⋊ #423 |
286 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#67532, #11771508, C3×#70063, … |
| maximal normal subgroup of | C3×#67532, #11771508, C3×#70063, … |
| maximal quotient of | C3×#70490, C3×#70491, C3×#70794, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4097);