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C5×#70347 #14297366

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#70347

Splittings

FittingC3×C5×#419 ⋊ C2
HallC3×C5 ⋊ #1796
SylowC3 ⋊ C5×#1796

Subgroups

subgroupG/H
centerC2×C5#4955
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#419C2
socleC2×C3×C5#379
prime radicalC2×C5×#1007C2
cosocleC22×C3×C4C23×C5
hypercenterC5×#419D3
hypocenterC3C5×#1796
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C5×#419

1072 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

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, 23064);