Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | SL(2,𝔽5) ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C42 | S5 |
| commutator, hypocenter | SL(2,𝔽5) | C2×C8 |
| Frattini | C2×C4 | C2×S5 |
| socle | C22 | C2×A5⋊C4 |
| prime radical | C2×#6732 | C4 |
| cosocle | C4×SL(2,𝔽5) | C22 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C42 | |
256 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 26 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:
(1,5,4,8,2,6,3,7)(9,30,20,26)(10,29,19,25)(11,32,17,28)(12,31,18,27)(13,15,14,16)(21,22)(23,24)(33,37,36,40,34,38,35,39)(41,62,52,58)(42,61,51,57)(43,64,49,60)(44,63,50,59)(45,47,46,48)(53,54)(55,56);(1,33)(2,34)(3,35)(4,36)(5,37)(6,38)(7,39)(8,40)(9,59,17,54,15,41,28,49,21,47,10,60,18,53,16,42,27,50,22,48)(11,58,19,56,14,43,25,51,23,46,12,57,20,55,13,44,26,52,24,45)(29,61,30,62)(31,63,32,64)96 conjugacy classes — view the full character table.
| maximal subgroup of | #72276774, #72276971, C8×GL(2,𝔽5) |
| maximal normal subgroup of | #72276774, #72276971, C8×GL(2,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240675);