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C5×#84019 #14457798

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#84019

Splittings

FittingC3×C5×#578 ⋊ C2
HallC3×C5 ⋊ #3289
SylowC3 ⋊ C5×#3289

Subgroups

subgroupG/H
centerC2×C5D4×#67
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#578C2
socleC2×C3×C5D42
hypercenterC5×#578D3
hypocenterC3C5×#3289
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×#578

896 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 40 points:

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

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 183496);