Finite Group Databasebeta

← Prev (#14415329) Next (#14415331) →

C5×#79480 #14415330

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

Aliases

direct productC5×#79480

Splittings

FittingC3×C5×#435 ⋊ C2
HallC3×C5 ⋊ #2932
SylowC3 ⋊ C5×#2932

Subgroups

subgroupG/H
centerC2×C4×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#435C2
socleC22×C3×C5C23×C4
prime radicalC5×#5548C2
cosocleC2×C3×C4C24×C5
hypercenterC5×#435D3
hypocenterC3C5×#2932
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C5×#435

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 141028);