Finite Group Databasebeta

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AGL(1,ℤ/16)×D71 #32150889

order18176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/16)×D71

Splittings

FittingC71×AGL(1,ℤ/16) ⋊ C2
SylowC71 ⋊ C2×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC2#442×D71
commutatorC8×C71C23×C4
FrattiniC2×C8C23×D71
FittingC71×AGL(1,ℤ/16)C2
socleC2×C71C2×#442
prime radical#509×D71C2
cosocleC2×C8×C71C24
hypercenterAGL(1,ℤ/16)D71
hypocenterC71C2×AGL(1,ℤ/16)
LCSG ▷ C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ AGL(1,ℤ/16)

710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1136

Conjugacy classes & character table

851 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 323005);