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C5×#67697 #14279149

order1920
automorphism?
homologyAbelianization (H1) = C42×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#67697

Splittings

HallC3×C5 ⋊ #1395
SylowC3 ⋊ C5×#1395

Subgroups

subgroupG/H
centerC4×C5#806
commutatorC2×C3×C4C42×C5
FrattiniC2×#41C2×C5×D3
FittingC3×C5×#410C2
socleC2×C3×C5#342
prime radicalC2×C3×C5×#41C22
cosocleC2×C3×#41C22×C5
hypercenterC5×#410D3
hypocenterC3C5×#1395
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C2×C5×#41 ◁ C5×#410

324 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 40 points:

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

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, 4847);