Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
No aliases for this group.
| derived | SL(2,𝔽9) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C4 | A6 |
| commutator, hypocenter | SL(2,𝔽9) | C2 |
| Frattini, socle, cosocle | C2 | C2×A6 |
| LCS | G ▷ SL(2,𝔽9) | |
| UCS | C1 ◁ C4 | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 80 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 80 points:
(1,2,8,25,16,6,11,28,45,46,24,38,43,15,17,7,12,29,13,3)(4,18,47,36,37,20,14,40,35,10,23,42,64,32,22,5,21,49,48,19)(9,30,59,51,58,33,61,72,55,27,54,76,73,56,57,34,62,78,63,31)(26,50,71,65,39,52,74,60,68,41,67,77,79,70,69,53,75,80,66,44);(1,4,6,20,24,23,7,5)(2,9,32,19,38,54,36,10)(3,14,41,25,46,21,44,15)(8,26,51,31,43,67,56,27)(11,33,48,37,12,34,35,22)(13,16,42,69,45,17,18,39)(28,52,55,58,29,53,63,57)(30,60,65,64,76,80,70,47)(40,61,79,68,49,62,71,66)(50,72,75,59,77,78,74,73)26 conjugacy classes — view the full character table.
| maximal subgroup of | #72209933, #72210857, #72224449, … |
| maximal normal subgroup of | #72210857, #72224449, #72224452, … |
| maximal quotient of | C4×SL(2,𝔽9), #72228177, #72228178 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4597);