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C5×#83416 #14425527

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×#83416

Splittings

FittingC3×C5×#536 ⋊ C2
HallC3×C5 ⋊ #3022
SylowC3 ⋊ C5×#3022

Subgroups

subgroupG/H
centerC2×C5C2×#937
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#536C2
socleC2×C3×C5C2×#120
prime radicalC5×#5964C2
hypercenterC5×#536D3
hypocenterC3C5×#3022
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C5×#536

1408 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)(9,13,15,14)(10,18,20,19)(11,23,24,27)(12,25,26,28)(16,21,30,33)(17,31,32,34)(22,37,39,38)(29,35,40,36);(9,12)(10,17)(11,22)(13,25)(14,28)(15,26)(16,29)(18,31)(19,34)(20,32)(21,35)(23,37)(24,39)(27,38)(30,40)(33,36);(7,8)(9,11)(10,16)(12,22)(13,23)(14,27)(15,24)(17,29)(18,21)(19,33)(20,30)(25,37)(26,39)(28,38)(31,35)(32,40)(34,36);(9,10,15,20)(11,21,24,33)(12,17,26,32)(13,19,14,18)(16,27,30,23)(22,36,39,35)(25,34,28,31)(29,37,40,38)

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 151225);