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C2×AGL(1,ℤ/8)×Dic43 #25960661

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

Aliases

direct productC2×AGL(1,ℤ/8)×Dic43

Splittings

SylowC43 ⋊ C2×C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC23C2×D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
Fitting, prime radicalC22×AGL(1,ℤ/8)×C43C2
socleC23×C43C22×D4
cosocleC2×C4×C43C25
hypercenterC22×AGL(1,ℤ/8)D43
hypocenterC43C2×C4×AGL(1,ℤ/8)
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×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, 1033632);