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AGL(1,ℤ/8)×Dic158 #35168844

order20224
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productAGL(1,ℤ/8)×Dic158

Splittings

SylowC79 ⋊ Q8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C22×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC4×AGL(1,ℤ/8)×C79C2
socleC22×C79C23×D4
prime radicalC2×AGL(1,ℤ/8)×C79C22
hypercenterC4×AGL(1,ℤ/8)D79
hypocenterC79Q8×AGL(1,ℤ/8)
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

2010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

1771 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 1050143);