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AGL(1,ℤ/8)×Dic142 #32878027

order18176
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productAGL(1,ℤ/8)×Dic142

Splittings

SylowC71 ⋊ Q8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C22×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC4×AGL(1,ℤ/8)×C71C2
socleC22×C71C23×D4
prime radicalC2×AGL(1,ℤ/8)×C71C22
hypercenterC4×AGL(1,ℤ/8)D71
hypocenterC71Q8×AGL(1,ℤ/8)
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

2010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

1595 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 1050143);