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AGL(1,ℤ/8)×C43⋊C8 #25066013

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×C43⋊C8

Splittings

SylowC43 ⋊ C8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4C2×D4×D43
commutatorC4×C43C23×C8
FrattiniC42C23×D43
FittingC4×AGL(1,ℤ/8)×C43C2
socleC22×C43C2×C4×D4
prime radicalC2×AGL(1,ℤ/8)×C43C4
cosocleC42×C43C24
hypercenterC4×AGL(1,ℤ/8)D43
hypocenterC43C8×AGL(1,ℤ/8)
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

802 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, 138984);