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C3×#10617417 #14413509

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

Aliases

direct productC3×#10617417

Splittings

FittingC3×C5×#131 ⋊ C4
HallC3×C5 ⋊ #2913
SylowC5 ⋊ C3×#2913

Subgroups

subgroupG/H
centerC2×C3C22×C4⋊AGL(1,𝔽5)
commutatorC4×C5C23×C3×C4
FrattiniC4C23×C3×AGL(1,𝔽5)
FittingC3×C5×#131C4
socleC2×C3×C5C22×C4⋊C4
prime radicalC3×D5×#41C22
cosocleC4×D5C24×C3
hypercenterC3×#131AGL(1,𝔽5)
hypocenterC5C3×#2913
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C3×#41 ◁ C3×#131

952 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, 139207);