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#16929807

order4352
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

No aliases for this group.

Splittings

SylowC17 ⋊ #9097

Subgroups

subgroupG/H
centerC2×C4#10587625
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC4×C17×AGL(1,ℤ/8)C2
socleC22×C17#386
prime radicalC2×C17×AGL(1,ℤ/8)C4
cosocleC2×C42×C17C23
hypercenterC4×AGL(1,ℤ/8)D17
hypocenterC17#9097
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Polycyclic presentation:

2^8,17|a^2=f,b^2=df,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^16,c^b=ch,d^b=dg,e^b=eg,f^b=fg,i^b=i^16,d^c=dg,e^c=eg,f^c=fg

Conjugacy classes & character table

404 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 65051);