Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#611 |
| Fitting | C22×C4×C9 ⋊ C2 |
| Sylow | C9 ⋊ C4×D4 |
141 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 141 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) = 17 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,6,8,7,2,4,3,9,5)(15,17);(2,4)(3,7)(5,6)(8,9)(14,15)(16,17);(10,11,12,13)84 conjugacy classes — view the full character table.
| maximal subgroup of | #611⋊C8, #10588410, #10588411, … |
| maximal normal subgroup of | #611⋊C8, #10588410, #10588411, … |
| maximal quotient of | C4×Dic9⋊C4, #10588613, C4×(C2×D9)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 138);