Finite Group DatabasebetaFinite Group Databasebeta| order | 7680 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#11757163⋊C2 |
| Fitting | C24×C4 ⋊ S5 |
| derived | #11757163 ⋊ C2×C4 |
1784 conjugacy classes of subgroups; only the 14 normal subgroups are shown.
This group has 1784 conjugacy classes of subgroups — too many to draw. Only its 14 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 20 |
A minimal faithful permutation representation — 2 generators on 14 points:
(1,2,3,4)(5,6,7,13,12)(8,11,9,10,14);(6,9,13,14,11,7,10,12)72 conjugacy classes — view the full character table.
| automorphism group of | C5×2−1+4 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3,4)(5,6,7,13,12)(8,11,9,10,14), (6,9,13,14,11,7,10,12));