Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C22 | C22×S5 |
| commutator, cosocle | C2×SL(2,𝔽5) | C23 |
| Fitting, hypercenter | C22⋊C4 | S5 |
| prime radical | C22⋊#6732 | C2 |
| hypocenter | SL(2,𝔽5) | #41 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
370 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Permutation generators:
(1,9,8,20,22,31,34,5)(2,3,37,17,18,23,16,39)(4,33,29,19,24,6,26,7)(10,27,14,30,32,36,13,21)(11,25,40,15,35,12,28,38)(41,46,42,45)(43,47,44,48)(49,53,82,79,70,68,56,57)(50,87,64,71,66,65,85,51)(52,55,74,54,72,67,77,81)(58,69,61,84,80,78,62,75)(59,86,76,60,83,63,88,73)(89,94,90,93)(91,95,92,96);(1,26,39,7,22,29,17,19)(2,28,37,8,18,40,16,34)(3,27,35,10,23,36,11,32)(4,25,38,6,24,12,15,33)(5,21,13,9,20,30,14,31)(41,48,42,47)(43,46,44,45)(49,75,61,56,70,84,62,82)(50,69,86,58,66,78,63,80)(51,73,87,57,71,60,65,79)(52,76,83,55,72,88,59,67)(53,74,85,54,68,77,64,81)(89,95,90,96)(91,93,92,94);(1,49)(2,50)(3,51)(4,52)(5,53)(6,54)(7,55)(8,56)(9,57)(10,58)(11,59)(12,60)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,70)(23,71)(24,72)(25,73)(26,74)(27,75)(28,76)(29,77)(30,78)(31,79)(32,80)(33,81)(34,82)(35,83)(36,84)(37,85)(38,86)(39,87)(40,88)(41,89)(42,90)(43,91)(44,92)(45,93)(46,94)(47,95)(48,96)48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240940);