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, Frattini | C2×C4 | C2×S5 |
| commutator, hypocenter | SL(2,𝔽5) | C2×C8 |
| Fitting, hypercenter | C42 | S5 |
| socle | C22 | C2×A5⋊C4 |
| prime radical | C2×#6732 | C4 |
| cosocle | C4×SL(2,𝔽5) | C22 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
238 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 24 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)(13,27,32,20)(14,28,31,19)(15,26,29,17)(16,25,30,18)(21,24,22,23)(33,37,36,40,34,38,35,39)(41,42)(43,44)(45,60,64,51)(46,59,63,52)(47,57,61,50)(48,58,62,49)(53,55,54,56);(1,37,4,40,2,38,3,39)(5,36,8,34,6,35,7,33)(9,50,11,52,10,49,12,51)(13,60,15,57,14,59,16,58)(17,44,19,41,18,43,20,42)(21,62,23,64,22,61,24,63)(25,46,27,48,26,45,28,47)(29,56,31,53,30,55,32,54)72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240676);