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 | C4⋊C4 | S5 |
| prime radical | C4⋊#6729 | C2 |
| hypocenter | SL(2,𝔽5) | #41 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
350 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Permutation generators:
(1,2,35,16,22,18,11,37)(3,4,8,6,23,24,34,33)(5,32,36,31,20,10,27,9)(7,25,15,29,19,12,38,26)(13,40,21,39,14,28,30,17)(45,47,54,51,66,67,76,63)(46,75,84,77,62,53,72,50)(48,82,58,64,68,59,57,49)(52,65,60,56,78,74,81,69)(55,83,73,71,79,61,70,80)(85,86)(87,88);(1,28,14,37,26,22,40,13,16,29)(2,10,35,34,4,18,32,11,8,24)(3,25,33,27,20,23,12,6,36,5)(7,38,39,31,30,19,15,17,9,21)(41,43,42,44)(45,77,53,47,81)(46,55,65,56,61)(48,71,70,64,52)(49,78,68,80,73)(50,75,67,60,66)(51,54,82,84,58)(57,63,76,59,72)(62,79,74,69,83)(85,88,86,87);(1,45,36,80,10,54)(2,46,20,64,25,69)(3,47)(4,48,33,77,28,72)(5,49,12,56,18,62)(6,50,40,84,24,68)(7,51,26,70,35,79)(8,52,14,58,21,65)(9,53,16,60,38,82)(11,55,19,63,29,73)(13,57,30,74,34,78)(15,59,31,75,37,81)(17,61)(22,66,27,71,32,76)(23,67)(39,83)(41,85)(42,86)(43,87)(44,88)48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240956);