Finite Group Databasebeta

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C5×#80128 #14454225

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#80128

Splittings

FittingC3×C5×#449 ⋊ C2
HallC3×C5 ⋊ #3268
SylowC3 ⋊ C5×#3268

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#449C2
socleC22×C3×C5C22×D4
hypercenterC5×#449D3
hypocenterC3C5×#3268
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#449

1020 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 28 points:

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

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, 179923);