Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×D4×Dic3 |
| Sylow | C32 ⋊ C4×D4 |
215 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 215 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,2,3)(5,6)(7,10,9,8);(4,5,6)(12,14);(11,12)(13,14)90 conjugacy classes — view the full character table.
| maximal subgroup of | #10591400, #10591401, #10591404, … |
| maximal normal subgroup of | #10591400, #10591401, #10591404, … |
| maximal quotient of | C3×Dic3×C22⋊C4, C3×#4950, C3×#4951, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 705);