Finite Group Databasebeta

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C5×#86626 #14483036

order1920
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C29

Aliases

direct productC5×#86626

Splittings

FittingC3×C5×#546 ⋊ C2
HallC3×C5 ⋊ D4×#41
SylowC3 ⋊ C5×D4×#41

Subgroups

subgroupG/H
centerC22×C5C24×D3
commutator, cosocleC22×C3C25×C5
FrattiniC22C24×C5×D3
FittingC3×C5×#546C2
socleC22×C3×C5C25
hypercenterC5×#546D3
hypocenterC3C5×D4×#41
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×#546

3296 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 5 generators on 20 points:

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

Conjugacy classes & character table

375 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 208734);