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 | C2×C4 | C22×A5 |
| commutator | C2×SL(2,𝔽5) | C23 |
| Frattini, socle, cosocle | C22 | C23×A5 |
| Fitting, hypercenter | C4×D4 | A5 |
| hypocenter | SL(2,𝔽5) | #41 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
577 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 577 conjugacy classes of subgroups — too many to draw. Only its 49 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)(29,52,48,31,51,37,32,46,42,36,49,43)(30,45,33,34,47,38,35,50,39,40,41,44);(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)(29,46,42,41,35,32,52,48,47,30)(31,49,43,45,40,36,51,37,50,34)(33,39)(38,44)(53,55,54,56);(1,29,2,30,21,49,16,44,22,50)(3,31,6,34,24,52,5,33,13,41)(4,32,7,35,23,51,10,38,17,45)(8,36,12,40,18,46,11,39,19,47)(9,37)(14,42)(15,43)(20,48)(25,53)(26,54)(27,55)(28,56)90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240962);