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Dic3×#4131 #14411508

order1920
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productDic3×#4131

Splittings

HallC3×C5 ⋊ C4×#131
SylowC5 ⋊ Dic3×#131
SylowC3 ⋊ C4×#4131

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FittingC2×C3×C5×D4C2×C4
socleC22×C3×C5C23×C4
prime radicalC2×C3×#711C22
cosocleC2×C3×Dic5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C4×#131
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

1144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137206);