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 |
| hypocenter | SL(2,𝔽5) | D4 |
| LCS | G ▷ #6732 ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
125 conjugacy classes of subgroups; only the 10 normal subgroups are shown.
This group has 125 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:
(1,11,34,27)(2,28)(3,6,12,21)(4,26,40,38)(5,45,31,23)(7,10)(8,48,16,14)(9,36,39,25)(13,41,43,32)(15,42,22,33)(17,35,37,24)(18,30,44,46);(1,32,29,6,42,36)(2,16,30,26,12,48)(3,47,13,40,37,34)(4,18,5,9,38,10)(7,33,44,14,35,22)(8,43,27,24,19,25)(11,39,20,17,45,21)(15,41,31,28,23,46)24 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11751521, #14515115, #14515117, … |
| maximal normal subgroup of | C2×#11751521, #14515115, #14515117, … |
| maximal quotient of | #14514932, #14514942, #14514965, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5716);