Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
| direct product | C2×#11715738 |
| Fitting | C2×#3573 ⋊ D3 |
2811 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 2811 conjugacy classes of subgroups — too many to draw. Only its 62 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:
(1,2)(3,5,9,6)(4,11,14,10)(7,18,20,17,22,32,21,16,19,15,8,31)(12,24,28,23,30,34,29,26,33,25,13,27);(3,33,5,34,9,28,6,27)(4,31,11,19,14,32,10,20)(7,30,15,24,21,13,17,26)(8,12,16,25,22,29,18,23);(4,10)(5,6)(7,19)(8,22)(11,14)(12,27)(13,26)(15,31)(17,32)(20,21)(23,33)(24,30)(25,28)(29,34)68 conjugacy classes — view the full character table.
| maximal subgroup of | #72342861, C2×#72215707, C2×#72236885, … |
| maximal normal subgroup of | #72342861, C2×#72215707, C2×#72236885, … |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2)(3,5,9,6)(4,11,14,10)(7,18,20,17,22,32,21,16,19,15,8,31)(12,24,28,23,30,34,29,26,33,25,13,27), (3,33,5,34,9,28,6,27)(4,31,11,19,14,32,10,20)(7,30,15,24,21,13,17,26)(8,12,16,25,22,29,18,23), (4,10)(5,6)(7,19)(8,22)(11,14)(12,27)(13,26)(15,31)(17,32)(20,21)(23,33)(24,30)(25,28)(29,34));