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 | C2×C4 | C2×S5 |
| commutator, cosocle | C2×SL(2,𝔽5) | C23 |
| Frattini, socle | C22 | C22×S5 |
| Fitting, hypercenter | C22×C4 | S5 |
| hypocenter | SL(2,𝔽5) | C2×D4 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
568 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Permutation generators:
(1,3)(2,4)(5,17,44,50,6,18,43,49)(7,41,45,12,8,42,46,11)(9,32,24,39,10,31,23,40)(13,29,16,27,14,30,15,28)(19,26,36,21,20,25,35,22)(33,51,38,47,34,52,37,48)(53,55)(54,56)(57,69,96,102,58,70,95,101)(59,93,97,64,60,94,98,63)(61,84,76,91,62,83,75,92)(65,81,68,79,66,82,67,80)(71,78,88,73,72,77,87,74)(85,103,90,99,86,104,89,100);(1,3,2,4)(5,52,14,46,19,23,6,51,13,45,20,24)(7,44,21,33,30,39,8,43,22,34,29,40)(9,37,28,36,17,42,10,38,27,35,18,41)(11,47,15,50,31,25,12,48,16,49,32,26)(53,55,54,56)(57,104,66,98,71,75,58,103,65,97,72,76)(59,96,73,85,82,91,60,95,74,86,81,92)(61,89,80,88,69,94,62,90,79,87,70,93)(63,99,67,102,83,77,64,100,68,101,84,78);(1,53)(2,54)(3,55)(4,56)(5,57,6,58)(7,59,8,60)(9,61,10,62)(11,63,12,64)(13,65,14,66)(15,67,16,68)(17,69,18,70)(19,71,20,72)(21,73,22,74)(23,75,24,76)(25,77,26,78)(27,79,28,80)(29,81,30,82)(31,83,32,84)(33,85,34,86)(35,87,36,88)(37,89,38,90)(39,91,40,92)(41,93,42,94)(43,95,44,96)(45,97,46,98)(47,99,48,100)(49,101,50,102)(51,103,52,104)66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240795);