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 | C22⋊S5 |
| commutator, cosocle | #6732 | C22 |
| Frattini | C4 | C2×S5 |
| Fitting, hypercenter | D4 | S5 |
| prime radical | #91881 | C2 |
| hypocenter | SL(2,𝔽5) | D4 |
| LCS | G ▷ #6732 ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
119 conjugacy classes of subgroups; only the 10 normal subgroups are shown.
This group has 119 conjugacy classes of subgroups — too many to draw. Only its 10 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 |
A minimal faithful permutation representation — 2 generators on 48 points:
(1,37,19,38,17,6)(2,36,27,20,33,5)(3,15,7,26,16,8)(4,14,42,18,34,11)(9,48,29,45,39,21)(10,32,44,46,40,23)(12,24,22,13,25,28)(30,35,31,47,43,41);(1,35,23,32,17,15,8,46,29,39,26,34,42,9,22,25,4,5,20,12,47,41,36,19)(2,45,21,40,33,27,11,10,44,31,18,14,7,43,30,24,3,16,38,13,28,48,37,6)24 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11751520, #14515115, #14515117, … |
| maximal normal subgroup of | C2×#11751520, #14515115, #14515117, … |
| maximal quotient of | #14514932, #14514941, #14514964, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5715);