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, cosocle | C4 | C22×A5 |
| commutator, hypocenter | SL(2,𝔽5) | C2×C4 |
| Fitting, hypercenter | M16 | A5 |
| socle | C2 | C2×C4×A5 |
| prime radical | C2×#6732 | C2 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C4 ◁ M16 | |
139 conjugacy classes of subgroups; only the 17 normal subgroups are shown.
This group has 139 conjugacy classes of subgroups — too many to draw. Only its 17 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:
(1,19,24,42,15,5,8,13,30,27)(2,35,40,16,12,9,23,37,6,4)(3,18,33,41,26)(7,34,47,14,20)(10,28,22,48,36)(11,17,44,45,25)(21,32)(29,39);(1,43,23,26,37,3,39,34,16,45,4,46,24,25,42,11,21,33,27,48,5,31,35,36,40,10,29,44,6,47,12,38,13,14,30,20,32,22,15,41)(2,17,8,28,9,7,19,18)48 conjugacy classes — view the full character table.
| maximal subgroup of | #14514940, #14514943, #14514944, … |
| maximal normal subgroup of | #14514940, #14514943, #14514944, … |
| maximal quotient of | #14514927, C22⋊#91145, C4⋊#91145, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5738);