Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C22 | C2×S5 |
| commutator, prime radical, cosocle | C2×SL(2,𝔽5) | C22 |
| Fitting, hypercenter | C2×C4 | S5 |
| hypocenter | SL(2,𝔽5) | Q8 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
105 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Permutation generators:
(1,4,2,3)(5,7,6,8)(13,14)(15,16)(17,35)(18,36)(19,34)(20,33)(21,44)(22,43)(23,41)(24,42)(25,48)(26,47)(27,45)(28,46)(29,37)(30,38)(31,39)(32,40);(1,8,2,7)(3,5,4,6)(9,20,24,42,45,14)(10,19,23,41,46,13)(11,18,21,43,47,15)(12,17,22,44,48,16)(25,33,37,26,34,38)(27,36,39)(28,35,40)(29,32)(30,31)33 conjugacy classes — view the full character table.
| maximal subgroup of | #14515028, #14515029, #14515035, … |
| maximal normal subgroup of | #14515028, #14515029, #14515035, … |
| maximal quotient of | C4⋊#91143, #14514967, C2×#11751517 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5712);