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C5×#78700 #14425311

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

Aliases

direct productC5×#78700

Splittings

FittingC2×C3×C5×#100 ⋊ C2
HallC3×C5 ⋊ #3019
SylowC3 ⋊ C5×#3019

Subgroups

subgroupG/H
centerC2×C5C2×#882
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC2×C3×C5×#100C2
socleC2×C3×C5C2×#120
hypercenterC2×C5×#100D3
hypocenterC3C5×#3019
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C2×C5×#100

1524 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 4 generators on 24 points:

(1,2,3,4,5)(6,7,8)(10,15)(14,23)(16,20)(17,24);(12,22)(16,20)(17,24)(18,21);(7,8)(9,11)(10,14)(12,21)(13,19)(15,23)(16,24)(17,20)(18,22);(7,8)(9,10)(11,17)(12,20)(13,15)(14,18)(16,22)(19,24)(21,23)

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, 151009);