Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C3×#5798 |
| Sylow | C32 ⋊ #518 |
794 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 794 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) = 48 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#70020, #11785909, C3×#70067, … |
| maximal normal subgroup of | C3×#70020, #11785909, C3×#70067, … |
| maximal quotient of | C3×#82083, C3×#82144, C3×#82317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7777);