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C2×AGL(1,ℤ/8)×#595 #17979759

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×AGL(1,ℤ/8)×#595
unambiguous semidirect productD17⋊(C4×AGL(1,ℤ/8))

Splittings

FittingC2×C17×AGL(1,ℤ/8) ⋊ C4
SylowC17 ⋊ C2×C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×D4×#595
commutatorC4×C17C24×C4
FrattiniC4C24×#595
FittingC2×C17×AGL(1,ℤ/8)C4
socleC22×C17C2×C4×D4
prime radicalC2×AGL(1,ℤ/8)×D17C2
cosocleC4×D17C25
hypercenterC2×AGL(1,ℤ/8)#595
hypocenterC17C2×C4×AGL(1,ℤ/8)
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

3242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1115003);