Finite Group DatabasebetaFinite Group Databasebeta| order | 3888 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22 |
| direct product | C2×#14517984 |
584 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 108 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2)(3,4,6)(7,10,15,9,13,11,12,8,14)(16,18,23,19,22,24,17,20,21);(4,5)(8,10,13)(11,15,14)(17,19)(18,24,20,21,22,23)150 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72220173 |
| 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)(3,4,6)(7,10,15,9,13,11,12,8,14)(16,18,23,19,22,24,17,20,21), (4,5)(8,10,13)(11,15,14)(17,19)(18,24,20,21,22,23));