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AGL(1,ℤ/8)×#1181 #16836247

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×#1181

Splittings

FittingC29×AGL(1,ℤ/8) ⋊ C4
SylowC29 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D4×#1181
commutatorC4×C29C23×C4
FrattiniC4C23×#1181
FittingC29×AGL(1,ℤ/8)C4
socleC2×C29C2×C4×D4
prime radicalAGL(1,ℤ/8)×D29C2
cosocleC4×D29C24
hypercenterAGL(1,ℤ/8)#1181
hypocenterC29C4×AGL(1,ℤ/8)
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 232

Conjugacy classes & character table

121 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 21265);