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C4×#14583167 #25103473

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#14583167

Splittings

FittingC4×AGL(1,ℤ/8)×C43 ⋊ C2
SylowC43 ⋊ C4×#472

Subgroups

subgroupG/H
centerC2×C4#13063297
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×AGL(1,ℤ/8)×C43C2
socleC22×C43C2×#121
prime radicalC2×#14583167C2
cosocleC22×C4×C43C24
hypercenterC4×AGL(1,ℤ/8)D43
hypocenterC43C4×#472
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

946 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 176444);