Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×#4936 |
| Sylow | C32 ⋊ #382 |
362 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#67738, C3×#67713, #11770922, … |
| maximal normal subgroup of | C3×#67738, C3×#67713, #11770922, … |
| maximal quotient of | C3×#71534, C3×#71535, C3×#69412, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3915);