Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#11714267 |
| derived | C22⋊(C22⋊A4) ⋊ C3×C4 |
1132 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 1132 conjugacy classes of subgroups — too many to draw. Only its 32 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) = 48 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(4,5,15,17,9,11,13,10)(6,18,8,12,14,19,7,16);(7,9,8)(11,16,12)(13,15,14)(17,19,18)72 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72215860, C3×#72215879, C3×#72215875 |
| maximal normal subgroup of | C3×#72215860, C3×#72215879, C3×#72215875 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(4,5,15,17,9,11,13,10)(6,18,8,12,14,19,7,16), (7,9,8)(11,16,12)(13,15,14)(17,19,18));