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 | D4×A5 |
| commutator | #6732 | C22 |
| Frattini, cosocle | C4 | C22×A5 |
| Fitting, hypercenter | D8 | A5 |
| hypocenter | SL(2,𝔽5) | D4 |
| LCS | G ▷ #6732 ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 96 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 96 points:
(1,51,15,67,62,17,52,14,19,92)(2,64,23,29,73,25,65,22,30,72)(3,41,82,5,27,36,42,81,6,75)(4,76,37,40,80)(7,54,49,9,39,46,11,88,10,84)(8,85,47,55,89)(12,59)(13,68,93,18,50)(16,74,61,86,91,38,90,35,66,96)(20,57)(21,28,71,26,63)(24,83,70,53,95,48,94,45,77,87)(31,44)(33,34)(58,79)(69,78);(1,56,5,78,6,43,17,69)(2,32,9,58,10,60,25,79)(3,47,14,70,15,21,36,45)(4,44,16,31,18,57,38,20)(7,13,22,35,23,37,46,61)(8,59,24,12,26,33,48,34)(11,40,29,66,30,68,54,86)(19,55,41,77,42,28,67,53)(27,80,51,91,52,93,75,96)(39,89,64,95,65,71,84,87)(49,63,72,83,73,85,88,94)(50,92,74,62,76,81,90,82)33 conjugacy classes — view the full character table.
| maximal subgroup of | #14515014, #14515016, #14515024, … |
| maximal normal subgroup of | #14515014, #14515016, #14515024, … |
| maximal quotient of | #14514956, #14514974, D8×SL(2,𝔽5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5740);