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AGL(1,ℤ/8)×#10624382 #37550476

order23168
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×#10624382

Splittings

FittingAGL(1,ℤ/8)×C181 ⋊ C4
SylowC181 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D4×#10624382
commutatorC4×C181C23×C4
FrattiniC4C23×#10624382
FittingAGL(1,ℤ/8)×C181C4
socleC2×C181C2×C4×D4
prime radicalAGL(1,ℤ/8)×D181C2
cosocleC4×D181C24
hypercenterAGL(1,ℤ/8)#10624382
hypocenterC181C4×AGL(1,ℤ/8)
LCSG ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1448

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 21265);