Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#942 |
| Fitting | C2×C32×Q8 ⋊ C2 |
| Sylow | C32 ⋊ #137 |
139 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 139 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2,3)(4,5,6)(7,20,11,10)(8,22,15,13)(9,19,17,16)(12,21,14,18);(7,17,11,9)(8,14,15,12)(10,16,20,19)(13,18,22,21);(5,6)(7,8)(9,12)(10,18)(11,15)(13,19)(14,17)(16,22)(20,21)63 conjugacy classes — view the full character table.
| maximal subgroup of | #10591641, #10591642, #10591643, … |
| maximal normal subgroup of | #10591641, #10591642, #10591643, … |
| maximal quotient of | C3×#4964, C3×#4966, C3×#4967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 713);