Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C4⋊S5 |
| commutator, cosocle | #6732 | C22 |
| Frattini | C4 | C2×S5 |
| Fitting, hypercenter | C8 | S5 |
| hypocenter | SL(2,𝔽5) | D4 |
| LCS | G ▷ #6732 ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
115 conjugacy classes of subgroups.
| minimal degree | μ(G) = 80 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 80 points:
(1,45,34,60,19,54,49,27,74,72,4,48,9,44,36,55,11,56,51,26,73,70,2,43)(3,39,33,75,13,58,67,22,12,66,78,23,8,47,37,76,18,59,68,24,14,65,77,28)(5,41,6,40,38,61,63,62,17,71,32,29,10,46,7,42,35,53,64,57,16,69,31,21)(15,79,52,25,20,80,50,30);(1,19,37,49,2,14)(3,5,36,38,78,50)(4,12,9,11,33,51)(6,7)(8,10,34,35,77,52)(13,20,68,63,74,32)(15,67,64,73,31,18)(21,53)(22,79,65,40,48,62)(23,72,26,28,70,27)(24,80,66,42,43,57)(25,75,69,56,41,47)(29,61)(30,76,71,54,46,39)(44,58,55)(45,59,60)27 conjugacy classes — view the full character table.
| maximal subgroup of | #14515013, #14515014, #14515017, … |
| maximal normal subgroup of | #14515013, #14515014, #14515017, … |
| maximal quotient of | #14514947, #14514963, #14515010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5689);