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C2×#20291472 #28329530

order13568
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#20291472
unambiguous semidirect productD53⋊#2946

Splittings

FittingC2×AGL(1,ℤ/8)×C53 ⋊ C4
SylowC53 ⋊ C2×#2946

Subgroups

subgroupG/H
centerC22C2×D4×#6157
commutatorC4×C53C24×C4
FrattiniC4C24×#6157
FittingC2×AGL(1,ℤ/8)×C53C4
socleC22×C53C2×C4×D4
prime radicalC2×AGL(1,ℤ/8)×D53C2
cosocleC4×D53C25
hypercenterC2×AGL(1,ℤ/8)#6157
hypocenterC53C2×#2946
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

2946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1696

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1115006);