Finite Group DatabasebetaFinite Group Databasebeta| order | 3840 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#11757163 |
| Fitting | C24×C4 ⋊ A5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #11757163 |
| commutator, hypocenter | #11757163 | C4 |
| Frattini | C2 | C2×#11757163 |
| Fitting | C24×C4 | A5 |
| socle, cosocle | C25 | C2×A5 |
| prime radical | C2×#11757163 | C2 |
| LCS | G ▷ #11757163 | |
| UCS | C1 ◁ C4 | |
441 conjugacy classes of subgroups; only the 9 normal subgroups are shown.
This group has 441 conjugacy classes of subgroups — too many to draw. Only its 9 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)(7,13,10,8,14,11)(9,12);(1,4,2,3)(5,12,10)(6,9,11)(7,8)48 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11757163⋊C2, #72266677, #72266684, … |
| maximal normal subgroup of | C4×#11757163⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2)(3,4)(7,13,10,8,14,11)(9,12), (1,4,2,3)(5,12,10)(6,9,11)(7,8));