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, prime radical, 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 | |
103 conjugacy classes of subgroups.
| minimal degree | μ(G) = 96 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 96 points:
(1,95,28,63,6,84,25,80)(2,74,34,93,10,89,46,81)(3,77,27,90,14,91,11,88)(4,55,42,54,16,69,40,49)(5,67,12,64,17,85,30,52)(7,87,20,56,21,70,38,71)(8,62,44,94,23,51,48,82)(9,79,35,96,24,61,18,92)(13,73,41,60,31,76,26,78)(15,68,29,65,32,86,43,53)(19,50,36,57,37,58,47,72)(22,75,45,66,39,59,33,83);(1,75,20,73,2,65,6,59,38,76,10,53)(3,68,18,94,25,57,14,86,35,82,28,72)(4,89,36,88,8,80,16,74,47,90,23,63)(5,51,21,78,9,49,17,62,7,60,24,54)(11,69,34,66,30,58,27,55,46,83,12,50)(13,84,33,96,40,70,31,95,45,92,42,87)(15,61,37,91,22,52,32,79,19,77,39,64)(26,85,44,81,43,71,41,67,48,93,29,56)27 conjugacy classes — view the full character table.
| maximal subgroup of | #14515015, #14515016, #14515018, … |
| maximal normal subgroup of | #14515015, #14515016, #14515018, … |
| maximal quotient of | #14514948, #14514963, #14515011, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5690);