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, Fitting, hypercenter | C8 | S5 |
| commutator, hypocenter | SL(2,𝔽5) | C2×C4 |
| Frattini | C4 | C2×S5 |
| socle | C2 | C4×S5 |
| prime radical | #91870 | C2 |
| cosocle | #6732 | C22 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C8 | |
114 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 12 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 48 |
Permutation generators:
(1,25,23,44,24,42,5,30,8,29,10,48,6,41,11,46,21,26,7,47,17,28,22,33)(2,37,13,43,36,34,4,18,15,40,16,35,9,31,3,45,20,38,14,32,12,39,27,19);(1,2,7,14,6,9,5,4)(3,17,15,11,13,8,12,23)(10,31,24,18,22,37,21,32)(16,30,36,25,27,47,20,41)(19,44,38,28,35,46,34,29)(26,43,48,39,42,45,33,40);(1,6)(2,9)(3,40,34,18)(4,14)(5,7)(8,44,33,25)(10,24,22,21)(11,29,42,30)(12,45,35,31)(13,39,38,32)(15,43,19,37)(16,36,27,20)(17,46,48,41)(23,28,26,47)48 conjugacy classes — view the full character table.
| maximal subgroup of | #14514986, #14514987, C2×#11751490, … |
| maximal normal subgroup of | #14514986, #14514987, C2×#11751490, … |
| maximal quotient of | #14514922, #14514937, #14514969, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5685);