Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#877 |
| Sylow | C32 ⋊ #117 |
169 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 169 conjugacy classes of subgroups — too many to draw. Only its 82 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 — 3 generators on 18 points:
(1,2,3)(4,5,6)(7,10,9,8)(13,17)(15,18);(11,13)(12,15)(14,17)(16,18);(5,6)(11,16,14,12)(13,18,17,15)90 conjugacy classes — view the full character table.
| maximal subgroup of | #10590405, C3×#4740, #10594024, … |
| maximal normal subgroup of | #10590405, C3×#4740, #10594024, … |
| maximal quotient of | C3×#4648, C3×#4649, C3×#4650, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 648);