Finite Group DatabasebetaFinite Group Databasebeta| order | 14976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | #1020×AGL(1,𝔽13) |
| Fitting, socle | C24×C13 ⋊ C3×C4×D3 |
| derived | C13×C22⋊A4 ⋊ C2×C3×C4 |
| Sylow | C13 ⋊ C3×C4×#1020 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C13×C22⋊A4 | C2×C3×C4 |
| Fitting, socle | C24×C13 | C3×C4×D3 |
| prime radical | D13⋊C3×#1020 | C2 |
| cosocle | D13×C22⋊A4 | C22×C3 |
| LCS | G ▷ C13×C22⋊A4 | |
| UCS | C1 | |
1782 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 1782 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 104 |
A minimal faithful permutation representation — 2 generators on 21 points:
(2,7,11,8,4,13,5,6,9,3,10,12)(14,17,16)(19,21,20);(1,2,6,4,11,8,12,13,3,9,10,7,5)(15,17)(18,19,21,20)130 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽13)×A4⋊S4 |
| maximal quotient of | AGL(1,𝔽13)×#5935, AGL(1,𝔽13)×#5934 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,7,11,8,4,13,5,6,9,3,10,12)(14,17,16)(19,21,20), (1,2,6,4,11,8,12,13,3,9,10,7,5)(15,17)(18,19,21,20));