Finite Group Databasebeta

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C5×#67696 #14279073

order1920
automorphism?
homologyAbelianization (H1) = C42×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×#67696

Splittings

HallC3×C5 ⋊ #1391
SylowC3 ⋊ C5×#1391

Subgroups

subgroupG/H
centerC4×C5#806
commutatorC23×C3C42×C5
FrattiniC2×#41C2×C5×D3
FittingC3×C5×#410C2
socleC2×C3×C5#342
prime radicalC2×C3×C5×#41C22
cosocleC2×C3×#41C22×C5
hypercenterC5×#410D3
hypocenterC3C5×#1391
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C2×C5×#41 ◁ C5×#410

332 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)(9,11,13,21,14,22,25,35)(10,15,18,28,16,19,30,33)(12,20,24,34,23,26,36,37)(17,31,32,40,29,27,38,39);(6,7,8)(9,10,12,17)(11,19,20,31)(13,18,24,32)(14,16,23,29)(15,26,27,22)(21,33,34,40)(25,30,36,38)(28,37,39,35)

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, 4771);