Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#4850 |
| Sylow | C32 ⋊ #477 |
211 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 211 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#68404, C3×#68260, #11779347, … |
| maximal normal subgroup of | C3×#68404, C3×#68260, #11779347, … |
| maximal quotient of | C3×#70485, C3×#68683, C3×#68624, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3829);