Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×S5 |
| commutator, hypocenter | SL(2,𝔽5) | C22×C4 |
| Frattini, socle | C22 | C22×S5 |
| Fitting, hypercenter | C42 | S5 |
| prime radical | C2×#91870 | C2 |
| cosocle | C2×SL(2,𝔽5) | C23 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
484 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 38 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:
(1,4,2,3)(5,23,30,9,28,7,22,32,11,25,6,24,29,10,27,8,21,31,12,26)(13,20,37,44,36,15,17,39,41,33,14,19,38,43,35,16,18,40,42,34)(45,48,46,47)(49,67,74,53,72,51,66,76,55,69,50,68,73,54,71,52,65,75,56,70)(57,64,81,88,80,59,61,83,85,77,58,63,82,87,79,60,62,84,86,78);(1,4,2,3)(5,33,12,26,6,34,11,25)(7,36,9,27,8,35,10,28)(13,42,24,31,14,41,23,32)(15,43,21,29,16,44,22,30)(17,40,20,37,18,39,19,38)(45,48,46,47)(49,77,56,70,50,78,55,69)(51,80,53,71,52,79,54,72)(57,86,68,75,58,85,67,76)(59,87,65,73,60,88,66,74)(61,84,64,81,62,83,63,82);(1,45)(2,46)(3,47)(4,48)(5,49,6,50)(7,51,8,52)(9,53,10,54)(11,55,12,56)(13,57,14,58)(15,59,16,60)(17,61,18,62)(19,63,20,64)(21,65,22,66)(23,67,24,68)(25,69,26,70)(27,71,28,72)(29,73,30,74)(31,75,32,76)(33,77,34,78)(35,79,36,80)(37,81,38,82)(39,83,40,84)(41,85,42,86)(43,87,44,88)72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240765);