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AGL(1,ℤ/8)×C22⋊D13 #16738506

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productAGL(1,ℤ/8)×C22⋊D13

Splittings

FittingC22×C13×AGL(1,ℤ/8) ⋊ C2
SylowC13 ⋊ D4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C22×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×AGL(1,ℤ/8)C2
socleC22×C13C23×D4
hypercenterC22×AGL(1,ℤ/8)D13
hypocenterC13D4×AGL(1,ℤ/8)
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

3230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1045155);