Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | D4×A5 |
| commutator | C4×SL(2,𝔽5) | C22 |
| Frattini, cosocle | C2×C4 | C22×A5 |
| Fitting, hypercenter | #107 | A5 |
| hypocenter | SL(2,𝔽5) | D8 |
| LCS | G ▷ C4×SL(2,𝔽5) ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #107 | |
252 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 21 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)(2,8)(3,16,13,14,23,9,21,7,15,22)(5,18,11,17,20,6,19,10,12,24)(25,31,28,29,26,32,27,30)(33,36)(34,40)(35,48,45,46,55,41,53,39,47,54)(37,50,43,49,52,38,51,42,44,56)(57,62,59,64,58,61,60,63);(1,41,14,36,9,47,4,35,15,33,3,46)(2,38,17,40,6,44,8,37,12,34,5,49)(7,56,21,45,24,48,13,52,16,39,20,53)(10,55,19,43,23,50,11,54,18,42,22,51)(25,61)(26,62)(27,63)(28,64)(29,59)(30,60)(31,58)(32,57)63 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240720);