Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| derived | SL(2,𝔽9) ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #13088278 |
| commutator, hypocenter | SL(2,𝔽9) | C4 |
| Frattini, Fitting, hypercenter | C4 | #10624296 |
| prime radical, cosocle | #13088280 | C2 |
| LCS | G ▷ SL(2,𝔽9) | |
| UCS | C1 ◁ C2 ◁ C4 | |
73 conjugacy classes of subgroups.
| minimal degree | μ(G) = 80 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 80 points:
(1,2,5,16,48)(3,9,27,45,41)(4,8,10,30,72)(6,19,55,73,71)(7,21,39,64,38)(11,34,17,51,65)(12,37,49,56,68)(13,40,36,67,47)(14,43,50,54,24)(15,46,28,18,53)(20,57,77,32,59)(22,61,60,76,79)(23,62,78,35,74)(25,52,58,75,80)(26,31,63,44,66)(29,69,42,33,70);(1,4,15,22,61,80,47,11,36,57,17,52,58,76,5,18)(2,8,26,20,7,23,64,24,67,77,69,72,55,49,6,9)(3,12,39,56,44,19,27,43,54,35,71,62,70,38,14,45)(10,33,46,40,53,79,78,29,32,63,51,48,34,25,68,66)(13,42,21,60,74,30,28,41,16,31,73,75,37,59,65,50)22 conjugacy classes — view the full character table.
| maximal subgroup of | #72224454 |
| maximal normal subgroup of | #72224454 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,5,16,48)(3,9,27,45,41)(4,8,10,30,72)(6,19,55,73,71)(7,21,39,64,38)(11,34,17,51,65)(12,37,49,56,68)(13,40,36,67,47)(14,43,50,54,24)(15,46,28,18,53)(20,57,77,32,59)(22,61,60,76,79)(23,62,78,35,74)(25,52,58,75,80)(26,31,63,44,66)(29,69,42,33,70), (1,4,15,22,61,80,47,11,36,57,17,52,58,76,5,18)(2,8,26,20,7,23,64,24,67,77,69,72,55,49,6,9)(3,12,39,56,44,19,27,43,54,35,71,62,70,38,14,45)(10,33,46,40,53,79,78,29,32,63,51,48,34,25,68,66)(13,42,21,60,74,30,28,41,16,31,73,75,37,59,65,50));