Finite Group Databasebeta

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C3×D5⋊#444 #14417940

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

Aliases

direct productC3×D5⋊#444
unambiguous semidirect productD5⋊(C3×#444)

Splittings

FittingC3×C5×#135 ⋊ C4
HallC3×C5 ⋊ C2×#444
SylowC5 ⋊ C2×C3×#444

Subgroups

subgroupG/H
centerC3×C4D4×AGL(1,𝔽5)
commutatorC4×C5C23×C3×C4
FrattiniC4C23×C3×AGL(1,𝔽5)
FittingC3×C5×#135C4
socleC2×C3×C5C2×C4×D4
prime radicalC3×D5×#135C2
cosocleC4×D5C24×C3
hypercenterC3×#135AGL(1,𝔽5)
hypocenterC5C2×C3×#444
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×#135

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 143638);