Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic3×#1094 |
926 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 130 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) = 72 |
A minimal faithful permutation representation — 2 generators on 22 points:
(1,2)(8,9,10)(11,12,13)(14,20,21,16,15,22,19,17,18);(3,4,5,6)(7,10)(8,9)(12,13)(15,17,20)(18,22,21)240 conjugacy classes — view the full character table.
| maximal subgroup of | #217×#1094, C2×#67×#1094 |
| maximal normal subgroup of | #217×#1094, C2×#67×#1094 |
| maximal quotient of | #217×#1094 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2)(8,9,10)(11,12,13)(14,20,21,16,15,22,19,17,18), (3,4,5,6)(7,10)(8,9)(12,13)(15,17,20)(18,22,21));