Finite Group Databasebeta

← Prev (#28319848) Next (#28319850) →

C2×#20290754 #28319849

order13568
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20290754
unambiguous semidirect productD53⋊#1907

Splittings

FittingC2×AGL(1,ℤ/8)×C53 ⋊ C4
SylowC53 ⋊ C2×#1907

Subgroups

subgroupG/H
centerC22#16811571
commutatorC2×C4×C53C23×C4
FrattiniC2×C4C23×#6157
FittingC2×AGL(1,ℤ/8)×C53C4
socleC22×C53#386
prime radicalC2×AGL(1,ℤ/8)×D53C2
cosocleC2×C4×D53C24
hypercenterC2×AGL(1,ℤ/8)#6157
hypocenterC53C2×#1907
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

1826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1696

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1105325);