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D11×AGL(1,ℤ/16) #14907210

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD11×AGL(1,ℤ/16)

Splittings

FittingC11×AGL(1,ℤ/16) ⋊ C2
SylowC11 ⋊ C2×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC2D11×#442
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×AGL(1,ℤ/16)C2
socleC2×C11C2×#442
prime radicalD11×#509C2
cosocleC2×C8×C11C24
hypercenterAGL(1,ℤ/16)D11
hypocenterC11C2×AGL(1,ℤ/16)
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ AGL(1,ℤ/16)

710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 176

Conjugacy classes & character table

161 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×AGL(1,ℤ/16), D11×#33688
maximal normal subgroup ofAGL(1,𝔽11)×AGL(1,ℤ/16), D11×#33688

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 323005);