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AGL(1,ℤ/8)×Dic86 #25977172

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productAGL(1,ℤ/8)×Dic86

Splittings

SylowC43 ⋊ Q8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC4×AGL(1,ℤ/8)×C43C2
socleC22×C43C23×D4
prime radicalC2×AGL(1,ℤ/8)×C43C22
hypercenterC4×AGL(1,ℤ/8)D43
hypocenterC43Q8×AGL(1,ℤ/8)
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

2010 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

979 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1050143);