Finite Group DatabasebetaFinite Group Databasebeta| order | 6912 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#72220122 |
| Fitting | C2×C32×C8 ⋊ GL(2,𝔽3) |
1584 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 1584 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 144 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,6,8,4,3,2)(5,7)(12,13,17,19,15,18,14,16);(10,11);(2,3)(4,9)(5,8)(13,16)(14,17)(18,19)104 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((1,6,8,4,3,2)(5,7)(12,13,17,19,15,18,14,16), (10,11), (2,3)(4,9)(5,8)(13,16)(14,17)(18,19));