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C5×#72098 #14307980

order1920
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#72098

Splittings

FittingC2×C3×C5×AGL(1,ℤ/8) ⋊ C2
HallC3×C5 ⋊ #2006
SylowC3 ⋊ C5×#2006

Subgroups

subgroupG/H
centerC22×C5#937
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C5×AGL(1,ℤ/8)C2
socleC22×C3×C5#120
hypercenterC2×C5×AGL(1,ℤ/8)D3
hypocenterC3C5×#2006
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×AGL(1,ℤ/8)

812 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 20 points:

(1,2,3,4,5)(6,7,8)(10,12)(13,14)(15,18)(16,20)(17,19);(7,8)(9,10)(11,12)(13,14)(15,20)(16,18)(17,19);(14,18)(15,16)(19,20)

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, 33678);