Finite Group Databasebeta

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C2×#19143834 #25962958

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#19143834

Splittings

FittingC22×AGL(1,ℤ/8)×C43 ⋊ C2
SylowC43 ⋊ C2×#3005

Subgroups

subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×AGL(1,ℤ/8)×C43C2
socleC23×C43C22×D4
hypercenterC22×AGL(1,ℤ/8)D43
hypocenterC43C2×#3005
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

5098 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, 1035929);