Finite Group Databasebeta

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C5×#69174 #14315298

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#69174

Splittings

FittingC3×C5×#357 ⋊ C2
HallC3×C5 ⋊ C4×D16
SylowC3 ⋊ C4×C5×D16

Subgroups

subgroupG/H
centerC22×C5D3×D8
commutatorC3×C8C22×C4×C5
FrattiniC2×C8C22×C5×D3
FittingC3×C5×#357C2
socleC22×C3×C5C2×D8
prime radicalC2×C5×#826C2
cosocleC2×C3×C8C23×C5
hypercenterC5×#357D3
hypocenterC3C4×C5×D16
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C2×C5×C8 ◁ C5×#357

348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 28 points:

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

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, 40996);