Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#11722396 |
982 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 982 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 108 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,4)(2,3)(5,6,7)(8,9,10)(12,14);(2,4)(9,10)(11,12)(13,14)(16,18)(17,21)(19,22)(20,23);(2,3,4)(15,22,23,17,16,18,21,20,19)234 conjugacy classes — view the full character table.
| maximal subgroup of | #72276569 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,4)(2,3)(5,6,7)(8,9,10)(12,14), (2,4)(9,10)(11,12)(13,14)(16,18)(17,21)(19,22)(20,23), (2,3,4)(15,22,23,17,16,18,21,20,19));