Finite Group Databasebeta

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C2×#19135865 #25124424

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19135865

Splittings

SylowC43 ⋊ C2×#2048

Subgroups

subgroupG/H
centerC22#14582813
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC22×AGL(1,ℤ/8)×C43C2
socleC22×C43#394
hypercenterC22×AGL(1,ℤ/8)D43
hypocenterC43C2×#2048
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

1450 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

970 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 197395);