Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C3 |
| direct product | #97×C3⋊S4 |
| Fitting | C22×C3×#97 ⋊ D3 |
1658 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1658 conjugacy classes of subgroups — too many to draw. Only its 191 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) = 288 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,4)(2,3)(5,6,7)(12,13,14,17,15,16,18,19);(2,4)(6,7);(2,3,4)(8,9,10,11)(13,16)(17,19)180 conjugacy classes — view the full character table.
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)(12,13,14,17,15,16,18,19), (2,4)(6,7), (2,3,4)(8,9,10,11)(13,16)(17,19));