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C2×Q16×ΓL(1,𝔽16) #14416155

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

Aliases

direct productC2×Q16×ΓL(1,𝔽16)
unambiguous semidirect productD5⋊(Dic3×Q16)

Splittings

FittingC2×C3×C5×Q16 ⋊ C4
HallC3×C5 ⋊ C2×C4×Q16
SylowC5 ⋊ C2×Dic3×Q16
SylowC3 ⋊ C2×Q16×AGL(1,𝔽5)

Subgroups

subgroupG/H
centerC22D4×ΓL(1,𝔽16)
commutatorC3×C4×C5C23×C4
FrattiniC4C23×ΓL(1,𝔽16)
FittingC2×C3×C5×Q16C4
socleC22×C3×C5C4×D4
prime radicalC22×C3×D5C2×D4
cosocleC3×C4×D5C24
hypercenterC2×Q16ΓL(1,𝔽16)
hypocenterC3×C5C2×C4×Q16
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 141853);