Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived | SL(2,𝔽5) ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C23 | C2×S5 |
| commutator, hypocenter | SL(2,𝔽5) | C42 |
| Fitting, hypercenter | C22×C4 | S5 |
| prime radical, cosocle | C22×SL(2,𝔽5) | C22 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
324 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
Permutation generators:
(1,50,2,49)(3,47,4,48)(5,82,18,74,38,57)(6,81,17,73,37,58)(7,86,15,53,40,61)(8,85,16,54,39,62)(9,59,41,89,26,69)(10,60,42,90,25,70)(11,51,36,64,28,84)(12,52,35,63,27,83)(13,87,43,72,23,55)(14,88,44,71,24,56)(19,77)(20,78)(21,76,34,68,29,79)(22,75,33,67,30,80)(31,65)(32,66)(45,92,46,91);(1,3,2,4)(5,32,38,18,6,31,37,17)(7,39,27,25,8,40,28,26)(9,36,30,33,10,35,29,34)(11,15,41,21,12,16,42,22)(13,24,44,20,14,23,43,19)(47,49,48,50)(51,77,84,63,52,78,83,64)(53,86,73,72,54,85,74,71)(55,81,76,80,56,82,75,79)(57,62,87,68,58,61,88,67)(59,69,90,65,60,70,89,66)72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240619);