Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | SL(2,𝔽5) ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C22 | C2×S5 |
| commutator, hypocenter | SL(2,𝔽5) | C2×C4 |
| Fitting, hypercenter | C2×C4 | S5 |
| prime radical | C2×#6729 | C2 |
| cosocle | C2×SL(2,𝔽5) | C22 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
135 conjugacy classes of subgroups; only the 14 normal subgroups are shown.
This group has 135 conjugacy classes of subgroups — too many to draw. Only its 14 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Permutation generators:
(1,4,2,3)(5,33,12,26,6,34,11,25)(7,36,9,27,8,35,10,28)(13,42,24,31,14,41,23,32)(15,43,21,29,16,44,22,30)(17,40,20,37,18,39,19,38);(1,4,2,3)(5,23,30,9,28,7,22,32,11,25,6,24,29,10,27,8,21,31,12,26)(13,20,37,44,36,15,17,39,41,33,14,19,38,43,35,16,18,40,42,34)36 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11751509, #14515067, C4×#91872, … |
| maximal normal subgroup of | C2×#11751509, #14515067, C4×#91872, … |
| maximal quotient of | #14514921, #14514939, #14514967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5704);