Finite Group DatabasebetaFinite Group Databasebeta| order | 23040 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C26 ⋊ ΓL(2,𝔽4) |
| derived | #72240854 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #72240854 | C2 |
| Frattini, socle | C24 | A4⋊S5 |
| Fitting | C26 | ΓL(2,𝔽4) |
| LCS | G ▷ #72240854 | |
| UCS | C1 | |
1160 conjugacy classes of subgroups; only the 8 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 8 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) = 20 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,14,20,8)(2,3,15,18)(4,6,11,10)(5,13,19,9)(7,16);(1,4,3,5)(2,9,10,8)(6,16)(7,14)(11,19,18,20)(12,15)(13,17)29 conjugacy classes — view the full character table.
| automorphism group of | #11757162, #14515302 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,14,20,8)(2,3,15,18)(4,6,11,10)(5,13,19,9)(7,16), (1,4,3,5)(2,9,10,8)(6,16)(7,14)(11,19,18,20)(12,15)(13,17));