Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | SL(2,𝔽9) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, Fitting, socle, hypercenter | C2 | PGL(2,𝔽9) |
| commutator, cosocle, hypocenter | SL(2,𝔽9) | C2 |
| LCS | G ▷ SL(2,𝔽9) | |
| UCS | C1 ◁ C2 | |
33 conjugacy classes of subgroups.
| minimal degree | μ(G) = 144 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 144 points:
(1,35,94,47,26,64,136,104)(2,19,30,46,28,67,6,103)(3,95,70,45,29,138,23,101)(4,141,14,43,27,118,53,85)(5,61,116,44,32,21,113,72)(7,81,73,40,18,39,98,25)(8,124,49,42,31,97,15,102)(9,88,115,41,10,127,76,100)(11,130,17,109,48,86,52,55)(12,62,59,140,50,89,108,105)(13,57,37,71,51,87,84,121)(16,80,90,58,54,33,63,110)(20,122,117,119,68,131,65,134)(22,107,144,79,60,132,133,74)(24,83,139,135,69,34,99,92)(36,96,143,77,75,128,126,112)(38,93,142,120,82,66,137,123)(56,125,114,78,111,106,129,91);(1,88,131,109,65,97,53,91,30,56)(2,133,5,48,43,39,104,52,70,83)(3,27,12,38,132,99,123,54,94,113)(4,50,82,107,139,120,16,136,116,29)(6,111,26,127,122,55,117,124,14,78)(7,20,134,73,93,9,44,101,49,142)(8,19,33,135,86,60,140,103,115,51)(10,72,45,15,137,18,68,119,98,66)(11,85,81,47,17,23,34,28,144,32)(13,31,67,80,92,130,22,105,46,76)(21,126,79,69,96,138,102,62,110,41)(24,128,95,42,89,58,100,61,143,74)(25,40)(35,36,121,129,125,87,77,118,59,90)(57,112,141,108,63,64,75,71,114,106)20 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#13088276 |
| maximal normal subgroup of | C5×#13088276 |
| maximal quotient of | C5×#13088276 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4593);