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D47×AGL(1,ℤ/16) #26369715

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD47×AGL(1,ℤ/16)

Splittings

FittingC47×AGL(1,ℤ/16) ⋊ C2
SylowC47 ⋊ C2×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC2#442×D47
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC47×AGL(1,ℤ/16)C2
socleC2×C47C2×#442
prime radical#509×D47C2
cosocleC2×C8×C47C24
hypercenterAGL(1,ℤ/16)D47
hypocenterC47C2×AGL(1,ℤ/16)
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ AGL(1,ℤ/16)

710 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

575 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 323005);