Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C4×#638 |
| Fitting | C22×C32×C4 ⋊ C2 |
| Sylow | C32 ⋊ C4×D4 |
282 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 97 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) = 144 |
A minimal faithful permutation representation — 3 generators on 14 points:
(6,8)(12,13,14);(5,6)(7,8)(10,11)(13,14);(1,2,3,4)(9,10,11)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10591051, #10591148, #10591149, … |
| maximal normal subgroup of | #10591051, #10591148, #10591149, … |
| maximal quotient of | C4×#3750, #10592632, C4×#3752, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 785);