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C2×AGL(1,ℤ/8)×#261 #16808354

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×AGL(1,ℤ/8)×#261
unambiguous semidirect productD13⋊(C4×AGL(1,ℤ/8))

Splittings

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

Subgroups

subgroupG/H
centerC22C2×D4×#261
commutatorC4×C13C24×C4
FrattiniC4C24×#261
FittingC2×C13×AGL(1,ℤ/8)C4
socleC22×C13C2×C4×D4
prime radicalC2×D13×AGL(1,ℤ/8)C2
cosocleC4×D13C25
hypercenterC2×AGL(1,ℤ/8)#261
hypocenterC13C2×C4×AGL(1,ℤ/8)
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

3242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#261×#453
maximal normal subgroup ofC2×#261×#453

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1115003);