Finite Group Databasebeta

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C4×#91989 #14319499

order1920
isoclinismisoclinic class of #6758
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#91989

Splittings

FittingC2×C3×C42×C5 ⋊ C4
HallC3×C5 ⋊ C4×#117
SylowC5 ⋊ C4×#926
SylowC3 ⋊ C4×#4130

Subgroups

subgroupG/H
centerC42C2×ΓL(1,𝔽16)
commutatorC2×C3×C5C22×C42
FrattiniC22C23×ΓL(1,𝔽16)
FittingC2×C3×C42×C5C4
socleC22×C3×C5C23×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC2×C42ΓL(1,𝔽16)
hypocenterC3×C5C4×#117
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C42 ◁ C2×C42

1504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45197);