Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, Fitting, hypercenter | C8 | S5 |
| commutator, hypocenter | SL(2,𝔽5) | C8 |
| socle | C2 | A5⋊C8 |
| prime radical | #6732 | C4 |
| cosocle | #91145 | C2 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C8 | |
55 conjugacy classes of subgroups.
| minimal degree | μ(G) = 96 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 96 points:
(1,39,7,41,18,16,10,37,14,45,5,8,20,13,34,32,24,47,27,48,6,22,21,26,35,4,2,19,3,33,17,23,38,31,46,15,9,36,11,44)(12,29,25,40,30,43,28,42)(49,84,62,91,82,64,55,61,73,96,53,85,75,90,83,80,68,74,78,81,54,95,51,77,94,52,69,79,76,92,65,67,59,88,66,63,86,89,60,93)(50,56,57,70,58,71,72,87);(1,67,42,76,34,79,32,55,28,91,33,62,17,95,43,78,18,74,16,86,30,88,48,59,6,85,40,73,46,61,15,69,25,77,45,51,5,84,29,60,35,89,4,68,12,90,44,75)(2,70,26,94,21,52,39,57,11,93,36,49,24,56,13,83,20,80,23,50,3,92,19,65,10,87,41,82,7,64,22,72,27,81,47,54,9,71,31,66,38,63,8,58,14,96,37,53)48 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11746443, #14514985, #14514986, … |
| maximal normal subgroup of | C2×#11746443, #14514985, #14514986, … |
| maximal quotient of | SL(2,𝔽5)⋊C16, C2×#11746443 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 638);