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C4×D4×ΓL(1,𝔽16) #14319568

order1920
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×D4×ΓL(1,𝔽16)

Splittings

FittingC3×C4×C5×D4 ⋊ C4
HallC3×C5 ⋊ C42×D4
SylowC5 ⋊ C4×D4×Dic3
SylowC3 ⋊ C4×D4×AGL(1,𝔽5)

Subgroups

subgroupG/H
centerC2×C4C22×ΓL(1,𝔽16)
commutatorC2×C3×C5C22×C42
FrattiniC22C23×ΓL(1,𝔽16)
FittingC3×C4×C5×D4C4
socleC22×C3×C5C23×C4
prime radicalC2×C3×D4×D5C22
cosocleC22×C3×D5C24
hypercenterC4×D4ΓL(1,𝔽16)
hypocenterC3×C5C42×D4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C4×D4

1848 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45266);