Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, Fitting, socle, hypercenter | C2 | PGL(2,𝔽9) |
| commutator, prime radical, cosocle, hypocenter | SL(2,𝔽9) | C2 |
| LCS | G ▷ SL(2,𝔽9) | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 160 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 160 points:
(1,114,77,99,46,159,60,82,72,131,4,95,75,88,21,154,31,87,71,153)(2,121,20,122,61,155,13,129,52,94,7,149,42,100,32,157,5,132,49,110)(3,136,65,130,37,143,58,150,16,83,10,156,62,105,63,117,78,123,36,90)(6,124,76,96,29,92,57,158,25,127,17,113,56,116,59,107,28,138,50,125)(8,112,69,140,23,151,30,85,15,133,19,141,41,111,48,152,14,93,34,147)(9,102,73,128,79,115,55,126,67,84,22,89,51,103,74,135,35,101,53,81)(11,86,26,160,68,144,12,146,40,98,24,97,54,148,80,118,27,119,18,120)(33,91,39,109,43,108,64,106,47,145,44,104,66,139,70,137,38,134,45,142);(1,156,33,158,17,108,3,114,4,136,44,138,6,137,10,95)(2,142,65,133,67,107,12,82,7,145,62,147,53,92,27,87)(5,106,24,120,47,121,9,128,13,134,11,98,45,149,22,103)(8,131,75,151,35,139,39,101,19,153,77,152,55,109,66,126)(14,83,64,129,46,160,56,115,30,90,38,132,21,148,76,135)(15,105,40,97,36,93,32,122,34,130,18,86,16,85,61,100)(20,155,74,116,58,117,59,81,42,157,79,96,78,143,29,84)(23,99,49,127,50,110,72,141,48,88,52,125,25,94,71,112)(26,154,73,89,31,146,37,150,54,159,51,102,60,119,63,123)(28,91,43,124,68,111,69,144,57,104,70,113,80,140,41,118)20 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4594);