Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | Dic3×D12 |
| Sylow | C32 ⋊ C4×D4 |
201 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 201 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 96 |
A minimal faithful permutation representation — 3 generators on 14 points:
(5,6,7,8)(9,10,11)(12,13,14);(6,8)(13,14);(1,2,3,4)(10,11)54 conjugacy classes — view the full character table.
| maximal subgroup of | #10590452, #10590453, #10590454, … |
| maximal normal subgroup of | #10590452, #10590453, #10590454, … |
| maximal quotient of | C3⋊C8×D12, #10590326, #10590337, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 540);