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 | #102 | A5 |
| hypocenter | SL(2,𝔽5) | D8 |
| LCS | G ▷ C4×SL(2,𝔽5) ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #102 | |
251 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 251 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:
(1,23,17,19,9)(2,20,15,16,6)(3,4,22,12,18)(5,8,24,14,21)(25,32,28,30,26,31,27,29)(33,54,49,50,41,36,55,44,51,35)(34,56,47,53,38,40,52,46,48,37)(39,45)(42,43)(57,61,59,63,58,62,60,64);(1,34)(2,36)(3,50)(4,40)(5,53)(6,48)(7,52)(8,33)(9,51)(10,54)(11,55)(12,47)(13,56)(14,44)(15,49)(16,37)(17,46)(18,41)(19,35)(20,45)(21,38)(22,43)(23,42)(24,39)(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, 240718);