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, cosocle | C22 | C23×A5 |
| commutator | C2×SL(2,𝔽5) | C23 |
| Fitting, hypercenter | #123 | A5 |
| hypocenter | SL(2,𝔽5) | #41 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ #123 | |
482 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 39 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:
(1,3,2,4)(5,17,6,18)(7,19,8,20)(9,30,47,24,49,25,13,37,44,34,10,29,48,23,50,26,14,38,43,33)(11,32,45,21,52,27,15,40,41,35,12,31,46,22,51,28,16,39,42,36)(53,56,54,55)(57,69,58,70)(59,71,60,72)(61,82,99,76,101,77,65,89,96,86,62,81,100,75,102,78,66,90,95,85)(63,84,97,73,104,79,67,92,93,87,64,83,98,74,103,80,68,91,94,88);(1,4,2,3)(5,13,36,20,32,49)(6,14,35,19,31,50)(7,16,34,18,29,51)(8,15,33,17,30,52)(9,45,23,28,38,42)(10,46,24,27,37,41)(11,48,21,26,40,44)(12,47,22,25,39,43)(53,56,54,55)(57,95,83,72,74,66)(58,96,84,71,73,65)(59,93,82,70,76,67)(60,94,81,69,75,68)(61,98,101,80,89,88)(62,97,102,79,90,87)(63,99,104,78,91,85)(64,100,103,77,92,86);(1,53)(2,54)(3,55)(4,56)(5,57)(6,58)(7,59)(8,60)(9,61,14,66,48,100,44,96,49,101)(10,62,13,65,47,99,43,95,50,102)(11,63,16,68,46,98,41,93,52,104)(12,64,15,67,45,97,42,94,51,103)(17,69)(18,70)(19,71)(20,72)(21,73,36,88,28,80,31,83,40,92)(22,74,35,87,27,79,32,84,39,91)(23,75,34,86,25,77,30,82,38,90)(24,76,33,85,26,78,29,81,37,89)66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240964);