Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
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 |
| hypocenter | SL(2,𝔽5) | C2×D4 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
469 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 469 conjugacy classes of subgroups — too many to draw. Only its 30 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:
(1,2,35,16,22,18,11,37)(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)(45,46,79,60,66,62,55,81)(47,48,52,50,67,68,78,77)(49,76,80,75,64,54,71,53)(51,69,59,73,63,56,82,70)(57,84,65,83,58,72,74,61);(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)(45,72,58,81,70,66,84,57,60,73)(46,54,79,78,48,62,76,55,52,68)(47,69,77,71,64,67,56,50,80,49)(51,82,83,75,74,63,59,61,53,65)(85,88,86,87);(1,45,22,66)(2,46,18,62)(3,47,23,67)(4,48,24,68)(5,49,20,64)(6,50,33,77)(7,51,19,63)(8,52,34,78)(9,53,31,75)(10,54,32,76)(11,55,35,79)(12,56,25,69)(13,57,14,58)(15,59,38,82)(16,60,37,81)(17,61,39,83)(21,65,30,74)(26,70,29,73)(27,71,36,80)(28,72,40,84)(41,85)(42,86)(43,87)(44,88)60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240852);