Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C2×S4×#1094 |
1962 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 1962 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2)(4,6,5)(7,8,10)(11,14,19,13,17,15,16,12,18);(3,6)(4,5)(8,9)(12,14,17)(15,19,18)200 conjugacy classes — view the full character table.
| maximal quotient of | C2×#72220173 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2)(4,6,5)(7,8,10)(11,14,19,13,17,15,16,12,18), (3,6)(4,5)(8,9)(12,14,17)(15,19,18));