Finite Group Databasebeta

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C22×#14583160 #25963968

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#14583160

Splittings

SylowC43 ⋊ C22×#471

Subgroups

subgroupG/H
centerC23#13063297
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
Fitting, prime radicalC22×AGL(1,ℤ/8)×C43C2
socleC23×C43#121
hypercenterC22×AGL(1,ℤ/8)D43
hypocenterC43C22×#471
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

2758 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, 1036939);