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, Fitting, hypercenter | C16 | A5 |
| commutator, hypocenter | SL(2,𝔽5) | C8 |
| Frattini, cosocle | C8 | C2×A5 |
| socle | C2 | C8×A5 |
| prime radical | #6732 | C4 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C16 | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 96 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 96 points:
(1,43,33,19,17,86,22,67,11,75,16,31,6,66,63,20,38,29,49,15,12,18,37,62,7,74,10,48,3,60,5,36,34,46,45,9,23,88,32,4,13,61,21,44,2,47,68,30)(8,92,73,55,24,89,58,77,35,95,80,72,27,96,70,56,52,71,85,78,42,54,94,69,28,76,41,84,53,87,26,93,39,82,51,40,59,91,65,25,81,90,57,50,14,83,79,64);(1,66,33,77,28,47,16,30,24,54,21,67,2,92,85,4,17,61,79,56,23,43,32,50,27,46,68,9,81,95,5,44,34,91,58,48,13,60,51,55,7,88,10,93,8,18,45,62,53,83,49,36,12,76,57,20,3,29,94,25,6,74,63,78,59,75,37,31,52,82,22,15,11,96,26,19,38,86,80,84)(14,89,70,69,39,90,73,72,42,87,65,64,35,71,41,40)72 conjugacy classes — view the full character table.
| maximal subgroup of | #14514915, #14514917, #14514986, … |
| maximal normal subgroup of | #14514915, #14514917, #14514986, … |
| maximal quotient of | C16×SL(2,𝔽5), C2×#11746446 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 641);