Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#4853 |
| Sylow | C32 ⋊ #441 |
234 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#69248, C3×#69309, #11797920, … |
| maximal normal subgroup of | C3×#69248, C3×#69309, #11797920, … |
| maximal quotient of | C3×#68517, C3×#68522, C3×#68524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3832);