Finite Group DatabasebetaFinite Group Databasebeta| order | 4992 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C23 |
| direct product | D13×#5935 |
| Fitting | C13×H(5,𝔽2) ⋊ C2×D3 |
| derived | C13×#997 ⋊ C22 |
| Sylow | C13 ⋊ C2×#5935 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D13×#1020 |
| commutator, cosocle, hypocenter | C13×#997 | C22 |
| Fitting | C13×H(5,𝔽2) | C2×D3 |
| socle | C2×C13 | C2×#1020 |
| LCS | G ▷ C13×#997 | |
| UCS | C1 ◁ C2 | |
666 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 666 conjugacy classes of subgroups — too many to draw. Only its 26 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:
(2,7,5)(3,8,6)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21);(1,5,7,2,4,8,3,6)(9,10,12,14,16,18,20,21,19,17,15,13,11)104 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊C3×#5935, #261×#5935 |
| maximal normal subgroup of | D13⋊C3×#5935, #261×#5935 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,7,5)(3,8,6)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21), (1,5,7,2,4,8,3,6)(9,10,12,14,16,18,20,21,19,17,15,13,11));