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 | #125 | A5 |
| prime radical | C2×#6732 | C22 |
| hypocenter | SL(2,𝔽5) | C2×Q8 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ #125 | |
456 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 41 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:
(1,9,16,8,20,11,4,15,10,3,14,5)(2,17,23,12,13,24,7,22,21,6,19,18)(25,26)(27,28)(29,51,33,31,46,38,32,49,39,36,52,44)(30,41,42,34,45,43,35,47,48,40,50,37)(53,54)(55,56);(1,15,23,19,11,4,9,21,13,5)(2,7)(3,20,18,22,16,8,14,24,17,10)(6,12)(25,27,26,28)(29,35,47,42,52)(30,41,48,46,32)(31,40,50,43,51)(34,45,37,49,36)(53,56,54,55);(1,29,4,32)(2,30,7,35)(3,31,8,36)(5,33,11,39)(6,34,12,40)(9,37,15,43)(10,38,16,44)(13,41,19,47)(14,42,20,48)(17,45,22,50)(18,46,24,52)(21,49,23,51)(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, 240909);