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 | Q16 | A5 |
| hypocenter | SL(2,𝔽5) | D4 |
| LCS | G ▷ #6732 ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
134 conjugacy classes of subgroups.
| minimal degree | μ(G) = 96 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 96 points:
(1,38,75,91,18,5,11,80,31,53,23,37,40,68,17,55,2,74,30,41,7,10,79,67,3,25,36,46,8,16,6,70,45,29,52,24,12,78,66,76)(4,71,82,93,50,19,33,48,64,13,26,35,73,92,42,57,9,14,63,51,21,32,47,65,15,56,39,81,28,44,20,72,77,62,54,22,34,49,69,43)(27,89,87,88,61,59,60,94)(58,95,90,86,85,83,84,96);(1,4,7,21)(2,46,83,91,18,9,49,94,92,50,12,80,95,67,3,34,14,88,62,15)(5,22,25,57)(6,26,23,20)(8,41,71,73,27,28,44,37,45,58,31,76,32,77,61,64,13,70,40,85)(10,79,90,66,53,35,82,87,63,43,38,75,84,30,16,72,47,60,69,51)(11,78,86,68,52,39,81,89,93,42,36,74,96,29,17,33,48,59,65,54)(19,55,56,24)33 conjugacy classes — view the full character table.
| maximal subgroup of | #14515013, #14515015, #14515023, … |
| maximal normal subgroup of | #14515013, #14515015, #14515023, … |
| maximal quotient of | #14514955, #14514974, #14515022, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5744);