Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | C2×#11711645 |
| Fitting | C2×#1791 ⋊ D3 |
1659 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 1659 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 3 generators on 34 points:
(3,15,31,12)(4,7,29,21)(5,20,25,8)(6,22,33,28)(9,11,19,16)(10,24,34,18)(13,27,30,23)(14,17,32,26);(3,4,6,10,9,5,13,14)(7,29,18,27,31,12,24,32,8,15,30,28,20,25,26,22,19,16,17,34,21,11,33,23);(1,2)56 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72236917, C2×#72236908, C2×#72236883, … |
| maximal normal subgroup of | C2×#72236917, C2×#72236908, C2×#72236883, … |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((3,15,31,12)(4,7,29,21)(5,20,25,8)(6,22,33,28)(9,11,19,16)(10,24,34,18)(13,27,30,23)(14,17,32,26), (3,4,6,10,9,5,13,14)(7,29,18,27,31,12,24,32,8,15,30,28,20,25,26,22,19,16,17,34,21,11,33,23), (1,2));