Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | D4×S5 |
| commutator, cosocle | #6732 | C23 |
| Frattini | C4 | C22×S5 |
| Fitting, hypercenter | D8 | S5 |
| hypocenter | SL(2,𝔽5) | C2×D4 |
| LCS | G ▷ #6732 ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
433 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 433 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.
| minimal degree | μ(G) = 96 |
| transitive degree | μt(G) = 96 |
Permutation generators:
(1,12,26,43,25,20,6,15,42,45,41,36)(2,11,38,28,37,10,9,23,34,29,31,22)(3,48,39,47,16,5,13,33,40,30,27,7)(4,17,19,44,18,21,14,8,35,46,32,24)(49,82,72,88,56,79,54,86,69,87,65,85)(50,81,84,92,63,78,57,96,68,94,60,95)(51,89,62,74,75,76,61,73,52,90,64,77)(53,83,58,93,59,80,55,67,70,91,71,66);(1,69,6,72)(2,68,9,84)(3,82,13,86)(4,75,14,64)(5,70,7,58)(8,81,17,96)(10,95,22,78)(11,90,23,74)(12,83,15,67)(16,80,27,66)(18,50,32,57)(19,91,35,93)(20,85,36,79)(21,73,24,89)(25,55,41,53)(26,76,42,77)(28,65,29,56)(30,49,47,54)(31,52,37,62)(33,92,48,94)(34,88,38,87)(39,60,40,63)(43,61,45,51)(44,71,46,59);(1,93,28,86,48,63)(2,77,39,96,35,71)(3,73,20,70,18,54)(4,94,43,74,38,56)(5,87,44,67,26,51)(6,91,29,82,33,60)(7,88,46,83,42,61)(8,85,10,75,25,57)(9,76,40,81,19,59)(11,66,21,84,30,62)(12,78,27,72,31,55)(13,89,36,58,32,49)(14,92,45,90,34,65)(15,95,16,69,37,53)(17,79,22,64,41,50)(23,80,24,68,47,52)45 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240860);