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, cosocle | C22 | C23×A5 |
| commutator | C2×SL(2,𝔽5) | C23 |
| Fitting, hypercenter | #121 | A5 |
| hypocenter | SL(2,𝔽5) | C2×D4 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ #121 | |
662 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 43 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)(5,12,6,11)(7,10,8,9)(13,21,14,22)(15,17,16,18)(19,24,20,23)(25,28,26,27)(29,31)(30,32)(33,39,34,40)(35,37,36,38)(41,50,42,49)(43,46,44,45)(47,51,48,52)(53,55,54,56);(1,4,2,3)(5,22,15,20,14,17,6,21,16,19,13,18)(7,27,12,26,9,23,8,28,11,25,10,24)(29,31,30,32)(33,50,43,48,42,45,34,49,44,47,41,46)(35,55,40,54,37,51,36,56,39,53,38,52);(1,29)(2,30)(3,31)(4,32)(5,33,6,34)(7,35,8,36)(9,37,10,38)(11,39,12,40)(13,41,14,42)(15,43,16,44)(17,45,18,46)(19,47,20,48)(21,49,22,50)(23,51,24,52)(25,53,26,54)(27,55,28,56)66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240874);