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C5×#80309 #14425772

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

Aliases

direct productC5×#80309

Splittings

FittingC3×C5×#458 ⋊ C2
HallC3×C5 ⋊ #3028
SylowC3 ⋊ C5×#3028

Subgroups

subgroupG/H
centerC2×C5D3×#120
commutator, cosocleC23×C3C24×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#458C2
socleC2×C3×C5C2×#120
prime radicalC5×#5966C2
hypercenterC5×#458D3
hypocenterC3C5×#3028
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C23×C5 ◁ C5×#458

1432 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)(7,8)(9,13,14,25)(10,17,18,24)(11,20,21,35)(12,22,23,37)(15,27,28,34)(16,29,30,36)(19,32,33,40)(26,38,31,39);(6,7,8)(9,12)(10,16)(11,19)(13,22)(14,23)(15,26)(17,29)(18,30)(20,32)(21,33)(24,36)(25,37)(27,38)(28,31)(34,39)(35,40);(9,11)(10,15)(12,19)(13,20)(14,21)(16,26)(17,27)(18,28)(22,32)(23,33)(24,34)(25,35)(29,38)(30,31)(36,39)(37,40);(9,10,14,18)(11,15,21,28)(12,16,23,30)(13,24,25,17)(19,31,33,26)(20,34,35,27)(22,36,37,29)(32,38,40,39)

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, 151470);