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C5×#78709 #14425386

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

Aliases

direct productC5×#78709

Splittings

FittingC2×C3×C5×#101 ⋊ C2
HallC3×C5 ⋊ #3020
SylowC3 ⋊ C5×#3020

Subgroups

subgroupG/H
centerC2×C5C2×#882
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC2×C3×C5×#101C2
socleC2×C3×C5C2×#120
hypercenterC2×C5×#101D3
hypocenterC3C5×#3020
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C2×C5×#101

1396 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)(10,17)(15,30)(16,31)(18,25)(19,33)(29,40)(32,34)(35,36);(9,12,14,24)(10,16,17,31)(11,20,22,38)(13,27,28,23)(15,29,30,40)(18,34,25,32)(19,35,33,36)(21,39,26,37);(7,8)(9,11)(10,15)(12,20)(13,26)(14,22)(16,29)(17,30)(18,33)(19,25)(21,28)(23,39)(24,38)(27,37)(31,40)(32,35)(34,36);(7,8)(9,10)(11,19)(12,16)(13,25)(14,17)(15,21)(18,28)(20,36)(22,33)(23,34)(24,31)(26,30)(27,32)(29,37)(35,38)(39,40)

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, 151084);