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AGL(1,ℤ/8)×Dic127 #30647540

order16256
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×Dic127

Splittings

SylowC127 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×D4×D127
commutatorC4×C127C23×C4
FrattiniC2×C4C23×D127
Fitting, prime radicalC2×AGL(1,ℤ/8)×C127C2
socleC22×C127C22×D4
cosocleC2×C4×C127C24
hypercenterC2×AGL(1,ℤ/8)D127
hypocenterC127C4×AGL(1,ℤ/8)
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

548 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1430 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 13320);