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#28303952

order13568
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

No aliases for this group.

Splittings

SylowC53 ⋊ #8954

Subgroups

subgroupG/H
centerC22#16811571
commutatorC2×C4×C53C22×C8
FrattiniC22×C4C22×#6157
Fitting, prime radicalC2×AGL(1,ℤ/8)×C53C4
socleC22×C53#386
cosocleC2×C4×Dic53C23
hypercenterC2×AGL(1,ℤ/8)#6157
hypocenterC53#8954
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

Polycyclic presentation:

2^8,53|a^2=f,b^2=dfg,d^2=g,e^2=g,f^2=h,b^a=bd,c^a=ce,e^a=eg,i^a=i^30,d^b=dg,f^b=fg,i^b=i^30,e^c=eg,i^f=i^52

Conjugacy classes & character table

350 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1089428);