Finite Group Databasebeta

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C3×C4×#4060 #14416659

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

Aliases

direct productC3×C4×#4060

Splittings

FittingC3×C4×C5×SD16 ⋊ C2
HallC3×C5 ⋊ C4×AGL(1,ℤ/8)
SylowC5 ⋊ C3×C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C3×C4D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC3×C4×C5×SD16C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4060C2
cosocleC2×C4×C5C24×C3
hypercenterC3×C4×SD16D5
hypocenterC5C3×C4×AGL(1,ℤ/8)
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4×SD16

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142357);