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 | D4×A5 |
| commutator | #6732 | C22 |
| Frattini, cosocle | C4 | C22×A5 |
| Fitting, hypercenter | SD16 | A5 |
| hypocenter | SL(2,𝔽5) | D4 |
| LCS | G ▷ #6732 ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C4 ◁ SD16 | |
133 conjugacy classes of subgroups; only the 13 normal subgroups are shown.
This group has 133 conjugacy classes of subgroups — too many to draw. Only its 13 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 96 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 96 points:
(1,4,5,15,6,16,17,32)(2,50,83,96,36,24,57,94,85,34,9,66,77,89,54,44,33,82,93,52,10,56,87,95,18,8,51,91,81,53,25,71,73,92,35,23,37,86,90,67)(3,46,43,76,19,30,27,41,49,59,13,62,7,69,39,48,28,42,65,72,14,26,21,80,40,12,47,61,55,38,31,45,22,64,60,29,11,20,70,58)(63,74,75,84,68,78,79,88);(1,65,22,17,55,21)(2,35,68,25,36,75)(3,90,33,31,85,57)(4,69,42)(5,49,43,6,70,7)(8,53,78)(9,18,79,10,54,63)(11,60,73,47,19,87)(12,92,50)(13,81,51,14,93,37)(15,76,61,32,80,41)(16,64,20)(23,52,88,44,67,84)(24,34,74)(26,38,82)(27,40,83,28,39,77)(29,95,66,48,96,71)(30,89,56)(45,72,91,62,58,94)(46,59,86)33 conjugacy classes — view the full character table.
| maximal subgroup of | #14515158, #14515160, #14515164, … |
| maximal normal subgroup of | #14515158, #14515160, #14515164, … |
| maximal quotient of | #14514955, #14514956, #14514973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5742);