Finite Group Databasebeta

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C5×#71101 #14291484

order1920
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#71101

Splittings

HallC3×C5 ⋊ #1669
SylowC3 ⋊ C5×#1669

Subgroups

subgroupG/H
centerC22×C5#939
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#474C2
socleC22×C3×C5#121
prime radicalC2×C3×C5×D4D4
hypercenterC5×#474D3
hypocenterC3C5×#1669
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#474

344 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 32 points:

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

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, 17182);