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C5×#71147 #14289811

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

Aliases

direct productC5×#71147

Splittings

HallC3×C5 ⋊ #1638
SylowC3 ⋊ C5×#1638

Subgroups

subgroupG/H
centerC22×C5#937
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#476C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC5×#476D3
hypocenterC3C5×#1638
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#476

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3,4,5)(6,7,8)(9,12,14,13)(10,16,17,21)(11,19,20,22)(15,23,24,18)(26,32)(28,29)(31,39)(33,34)(35,40)(36,37);(7,8)(9,11)(10,15)(12,19)(13,22)(14,20)(16,23)(17,24)(18,21)(25,27,30,38)(26,31,34,40)(28,37,29,36)(32,39,33,35);(9,10,14,17)(11,18,20,23)(12,16,13,21)(15,22,24,19)(25,26,30,34)(27,35,38,39)(28,33,29,32)(31,37,40,36)

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 15509);