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C5×#72124 #14316448

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

Aliases

direct productC5×#72124

Splittings

FittingC3×C5×#578 ⋊ C2
HallC3×C5 ⋊ #2193
SylowC3 ⋊ C5×#2193

Subgroups

subgroupG/H
centerC2×C5#5217
commutator, cosocleC2×C3×C8C23×C5
FrattiniC2×C8C22×C5×D3
FittingC3×C5×#578C2
socleC2×C3×C5#447
hypercenterC5×#578D3
hypocenterC3C5×#2193
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×#131 ◁ C5×#578

420 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)(6,7,8)(9,11,15,22)(10,17,19,34)(12,21,26,37)(13,27,14,20)(16,29,30,40)(18,33,28,32)(23,36,25,39)(24,38,35,31);(9,10)(11,17)(12,24)(13,18)(14,28)(15,19)(16,23)(20,32)(21,38)(22,34)(25,30)(26,35)(27,33)(29,36)(31,37)(39,40);(7,8)(10,16)(11,20)(12,23)(13,14)(17,31)(18,35)(19,30)(21,37)(22,27)(24,28)(25,26)(29,32)(33,40)(34,38)

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, 42146);