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 | #11751514 | C2 |
| hypocenter | SL(2,𝔽5) | #41 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
346 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 346 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) = 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)(45,61,48,69,66,83,68,56)(46,49,73,74,62,64,70,65)(47,58,75,79,67,57,53,55)(50,81,59,54,77,60,82,76)(51,78,80,84,63,52,71,72)(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)(85,87,86,88);(1,45,19,63,31,75,22,66,7,51,9,53)(2,46,15,59,26,70,18,62,38,82,29,73)(3,47,13,57,34,78,23,67,14,58,8,52)(4,48,28,72,39,83,24,68,40,84,17,61)(5,49,32,76,16,60,20,64,10,54,37,81)(6,50,33,77)(11,55,27,71,25,69,35,79,36,80,12,56)(21,65,30,74)(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, 240927);