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C2×AGL(1,ℤ/8)×#64408 #34031419

order18688
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×AGL(1,ℤ/8)×#64408
unambiguous semidirect productD73⋊(C4×AGL(1,ℤ/8))

Splittings

FittingC2×AGL(1,ℤ/8)×C73 ⋊ C4
SylowC73 ⋊ C2×C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×D4×#64408
commutatorC4×C73C24×C4
FrattiniC4C24×#64408
FittingC2×AGL(1,ℤ/8)×C73C4
socleC22×C73C2×C4×D4
prime radicalC2×AGL(1,ℤ/8)×D73C2
cosocleC4×D73C25
hypercenterC2×AGL(1,ℤ/8)#64408
hypocenterC73C2×C4×AGL(1,ℤ/8)
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

3242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1168

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1115003);