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AGL(1,ℤ/8)×Dic166 #36284979

order21248
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productAGL(1,ℤ/8)×Dic166

Splittings

SylowC83 ⋊ Q8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C22×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC4×AGL(1,ℤ/8)×C83C2
socleC22×C83C23×D4
prime radicalC2×AGL(1,ℤ/8)×C83C22
hypercenterC4×AGL(1,ℤ/8)D83
hypocenterC83Q8×AGL(1,ℤ/8)
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

2010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

1859 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1050143);