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C5×#69312 #14314501

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

Aliases

direct productC5×#69312

Splittings

FittingC3×C5×#365 ⋊ C2
HallC3×C5 ⋊ #2155
SylowC3 ⋊ C5×#2155

Subgroups

subgroupG/H
centerC2×C5D3×#106
commutatorC3×C8C22×C4×C5
FrattiniC2×C8C22×C5×D3
FittingC3×C5×#365C2
socleC2×C3×C5C2×#106
prime radicalC22×C5×D3SD16
cosocleC2×C3×C8C23×C5
hypercenterC5×#365D3
hypocenterC3C5×#2155
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×C8 ◁ C5×#365

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 480

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

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

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 40199);