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C2×#13130875 #16798676

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13130875
unambiguous semidirect productD13⋊#1907

Splittings

FittingC2×C13×AGL(1,ℤ/8) ⋊ C4
SylowC13 ⋊ C2×#1907

Subgroups

subgroupG/H
centerC22#11719150
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×AGL(1,ℤ/8)C4
socleC22×C13#386
prime radicalC2×D13×AGL(1,ℤ/8)C2
cosocleC2×C4×D13C24
hypercenterC2×AGL(1,ℤ/8)#261
hypocenterC13C2×#1907
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

1826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1105325);