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C4×AGL(1,ℤ/8)×D43 #25960653

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×AGL(1,ℤ/8)×D43

Splittings

FittingC4×AGL(1,ℤ/8)×C43 ⋊ C2
SylowC43 ⋊ C2×C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4C2×D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC4×AGL(1,ℤ/8)×C43C2
socleC22×C43C23×D4
prime radicalC2×AGL(1,ℤ/8)×D43C2
cosocleC2×C4×C43C25
hypercenterC4×AGL(1,ℤ/8)D43
hypocenterC43C2×C4×AGL(1,ℤ/8)
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

3242 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033624);