Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C3×#5812 |
| Sylow | C32 ⋊ #519 |
610 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 382 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#70101, #11785945, C3×#69672, … |
| maximal normal subgroup of | C3×#70101, #11785945, C3×#69672, … |
| maximal quotient of | C3×#82144, C3×#82450, C3×#84062, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7791);