Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×#817 |
| Sylow | C32 ⋊ C2×#106 |
298 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 298 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×#67816, C3×#67730, #11772427, … |
| maximal normal subgroup of | C3×#67816, C3×#67730, #11772427, … |
| maximal quotient of | C2×C3×#4457, C3×#69730, C3×#70749, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4083);