Finite Group Databasebeta

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C3×#10615661 #14417007

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

Aliases

direct productC3×#10615661

Splittings

HallC3×C5 ⋊ #2946
SylowC5 ⋊ C3×#2946

Subgroups

subgroupG/H
centerC22×C3C2×D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
Fitting, prime radicalC2×C3×C5×AGL(1,ℤ/8)C2
socleC22×C3×C5C22×D4
cosocleC2×C4×C5C24×C3
hypercenterC2×C3×AGL(1,ℤ/8)D5
hypocenterC5C3×#2946
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×AGL(1,ℤ/8)

1012 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142705);