Finite Group Databasebeta

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C5×#79774 #14416835

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#79774

Splittings

FittingC3×C5×#440 ⋊ C2
HallC3×C5 ⋊ C4×#137
SylowC3 ⋊ C4×C5×#137

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutatorC3×C4C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#440C2
socleC22×C3×C5C22×D4
prime radicalC2×C5×#237C22
cosocleC2×C3×C4C24×C5
hypercenterC5×#440D3
hypocenterC3C4×C5×#137
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#440

968 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142533);