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AGL(1,ℤ/8)×#10596842 #34034527

order18688
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×#10596842

Splittings

FittingAGL(1,ℤ/8)×C73 ⋊ C8
SylowC73 ⋊ C8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D4×#10596842
commutatorC4×C73C23×C8
FrattiniC4C23×#10596842
FittingAGL(1,ℤ/8)×C73C8
socleC2×C73C2×C8×D4
prime radicalAGL(1,ℤ/8)×D73C4
cosocleC4×#64408C24
hypercenterAGL(1,ℤ/8)#10596842
hypocenterC73C8×AGL(1,ℤ/8)
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 584

Conjugacy classes & character table

187 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1118111);