Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×#72220152 |
4236 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 3 generators on 22 points:
(4,6)(7,8)(9,10)(11,12,13)(15,18,22)(17,21,19);(1,2)(8,9,10)(14,22,21,16,15,17,20,18,19);(3,4)(5,6)(8,9)(12,13)(15,17)(16,20)(18,21)(19,22)276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72220160, C22×#72220152 |
| maximal normal subgroup of | C22×#72220152 |
| maximal quotient of | C2×#72252958, C22×#72220152 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((4,6)(7,8)(9,10)(11,12,13)(15,18,22)(17,21,19), (1,2)(8,9,10)(14,22,21,16,15,17,20,18,19), (3,4)(5,6)(8,9)(12,13)(15,17)(16,20)(18,21)(19,22));