Finite Group Databasebeta

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C3×D5⋊#410 #14411930

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC3×D5⋊#410
unambiguous semidirect productD5⋊(C3×#410)

Splittings

FittingC2×C3×C5×#41 ⋊ C4
HallC3×C5 ⋊ C2×#410
SylowC5 ⋊ C2×C3×#410

Subgroups

subgroupG/H
centerC3×C4C2×C22⋊AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC2×C3×C5×#41C4
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×C3×D5×#41C2
cosocleC22×D5C24×C3
hypercenterC2×C3×#41AGL(1,𝔽5)
hypocenterC5C2×C3×#410
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#41

1576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137628);