Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#2032⋊C3 |
| Fitting, Sylow | C4×#2032 ⋊ C3 |
| derived | #543 ⋊ C2×C3×C4 |
697 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 697 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3,4)(7,13,8)(10,16,11)(14,20,15)(17,18,19);(5,18,9,16)(6,13)(7,11)(8,17,15,10)(12,20)(14,19)84 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#72209831 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3,4)(7,13,8)(10,16,11)(14,20,15)(17,18,19), (5,18,9,16)(6,13)(7,11)(8,17,15,10)(12,20)(14,19));