Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
| direct product | C2×#11715735 |
| Fitting | C2×#3573 ⋊ D3 |
2878 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 2878 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:
(3,4,8,12)(5,14,13,9)(6,23,18,10)(7,32)(11,17)(15,20,25,27)(16,31)(19,22)(21,33)(24,30)(26,34)(28,29);(3,6,17,7)(4,20,22,21)(5,25,29,26)(8,18,30,19)(9,10,31,11)(12,27,32,28)(13,15,33,16)(14,23,34,24);(1,2)68 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72236876, C2×#72236886, C2×#72236883, … |
| maximal normal subgroup of | C2×#72236876, C2×#72236886, C2×#72236883, … |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((3,4,8,12)(5,14,13,9)(6,23,18,10)(7,32)(11,17)(15,20,25,27)(16,31)(19,22)(21,33)(24,30)(26,34)(28,29), (3,6,17,7)(4,20,22,21)(5,25,29,26)(8,18,30,19)(9,10,31,11)(12,27,32,28)(13,15,33,16)(14,23,34,24), (1,2));