Finite Group Databasebeta

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C5×#79165 #14416212

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

Aliases

direct productC5×#79165

Splittings

FittingC3×C5×#427 ⋊ C2
HallC3×C5 ⋊ C4×#135
SylowC3 ⋊ C4×C5×#135

Subgroups

subgroupG/H
centerC2×C4×C5D3×D4
commutatorC3×C4C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#427C2
socleC22×C3×C5C22×D4
prime radicalC2×C5×#904C2
cosocleC2×C3×C4C24×C5
hypercenterC5×#427D3
hypocenterC3C4×C5×#135
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C5×#427

1000 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)(6,7,8)(13,16,18,17)(14,20,21,25)(15,23,24,26)(19,27,28,22);(7,8)(9,11,12,10);(7,8)(13,15)(14,19)(16,23)(17,26)(18,24)(20,27)(21,28)(22,25);(9,10,12,11)(13,14)(15,22)(16,20)(17,25)(18,21)(19,23)(24,27)(26,28)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 141910);