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C5×#68427 #14285168

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#68427

Splittings

FittingC3×C5×#332 ⋊ C2
HallC3×C5 ⋊ #1554
SylowC3 ⋊ C5×#1554

Subgroups

subgroupG/H
centerC22×C5D3×C22⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#332C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C5×D3C22⋊C4
cosocleC3×C42C23×C5
hypercenterC5×#332D3
hypocenterC3C5×#1554
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#332

396 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3,4,5)(7,8)(9,12,14,13)(10,16,17,21)(11,19,20,22)(15,23,18,24)(26,31)(30,39)(32,36)(33,40);(6,7,8)(9,11,14,20)(10,15,17,18)(12,19,13,22)(16,23,21,24)(25,27,29,35)(26,30,31,39)(28,37,38,34)(32,40,36,33);(9,10,13,16,14,17,12,21)(11,18,19,23,20,15,22,24)(25,26)(27,33)(28,36)(29,31)(30,34)(32,38)(35,40)(37,39)

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 10866);