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C5×#83957 #14425446

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

Aliases

direct productC5×#83957

Splittings

FittingC2×C3×C5×AGL(1,ℤ/8) ⋊ C2
HallC3×C5 ⋊ #3021
SylowC3 ⋊ C5×#3021

Subgroups

subgroupG/H
centerC2×C5C2×#937
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC2×C3×C5×AGL(1,ℤ/8)C2
socleC2×C3×C5C2×#120
hypercenterC2×C5×AGL(1,ℤ/8)D3
hypocenterC3C5×#3021
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C2×C5×AGL(1,ℤ/8)

1472 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)(9,12,14,13)(10,15,17,20)(11,18,19,21)(16,22,24,23);(7,8)(9,11)(10,16)(12,18)(13,21)(14,19)(15,22)(17,24)(20,23);(9,10)(11,16)(12,15)(13,20)(14,17)(18,22)(19,24)(21,23);(10,15)(12,13)(16,23)(17,20)(18,21)(22,24)

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, 151144);