Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#832 |
| Sylow | C32 ⋊ #102 |
127 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 127 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.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2,3)(4,5,6)(12,15)(13,18)(16,17);(5,6)(7,10,9,8)(11,12)(13,15)(14,17)(16,18)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10591400, #10591401, #10591402, … |
| maximal normal subgroup of | #10591400, #10591401, #10591402, … |
| maximal quotient of | C3×#4529, C3×D4⋊(C3⋊C8), C3×#4537, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 266);