Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C22 | C2×S5 |
| commutator, hypocenter | SL(2,𝔽5) | C2×C4 |
| Fitting, hypercenter | C23 | S5 |
| prime radical | C22×SL(2,𝔽5) | C2 |
| cosocle | C2×SL(2,𝔽5) | C22 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C23 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Permutation generators:
(1,4,2,3)(5,52,27,38,6,51,28,37)(7,41,44,12,8,42,43,11)(9,40,36,18,10,39,35,17)(13,34,46,16,14,33,45,15)(19,26,29,23,20,25,30,24)(21,47,49,32,22,48,50,31);(5,7,27,35,45,6,8,28,36,46)(9,14,32,24,48,10,13,31,23,47)(11,40,16,42,49)(12,39,15,41,50)(17,33,20,38,30)(18,34,19,37,29)(25,26)(43,44)36 conjugacy classes — view the full character table.
| maximal subgroup of | #14514936, #14514945, C2×#11751530, … |
| maximal normal subgroup of | #14514936, #14514945, C2×#11751530, … |
| maximal quotient of | #14514921, C22⋊#91143, #14514959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5725);