Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #4451 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#4465 |
| Sylow | C32 ⋊ #330 |
140 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 50 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×D3×#330, C2×C3×#4465, D3×#4465, … |
| maximal normal subgroup of | C3×D3×#330, C2×C3×#4465, D3×#4465, … |
| maximal quotient of | C3×#67477, C3×#67478, C3×#67659, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1091);