Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#11710965 |
| derived | #543⋊C3 ⋊ C3×C4 |
318 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 26 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)(4,15,13,18)(5,19,9,7,11,14,12,16)(6,10,8,17);(6,7,14)(9,10,17)(12,18,15)(13,16,19)81 conjugacy classes — view the full character table.
| maximal subgroup of | #72227496 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(4,15,13,18)(5,19,9,7,11,14,12,16)(6,10,8,17), (6,7,14)(9,10,17)(12,18,15)(13,16,19));