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C49×C3⋊AGL(1,𝔽13) #37524199

order22932
automorphism?
homologyAbelianization (H1) = C3×C4×C49 · Schur multiplier (H2) = C1

Aliases

direct productC49×C3⋊AGL(1,𝔽13)
unambiguous semidirect productC3⋊(C49×AGL(1,𝔽13))
unambiguous semidirect product(C3⋊#261)⋊(C3×C49)

Splittings

FittingC3×C13×C49 ⋊ C3×C4
derivedC3×C13 ⋊ C3×C4×C49
HallC3×C13⋊C3×C49 ⋊ C4
HallC13×C49 ⋊ C3×Dic3
HallC3×C13⋊C3 ⋊ C4×C49
SylowC13 ⋊ C3×Dic3×C49

Subgroups

subgroupG/H
center, hypercenterC49C3⋊AGL(1,𝔽13)
commutator, hypocenterC3×C13C3×C4×C49
FrattiniC7C7×C3⋊AGL(1,𝔽13)
FittingC3×C13×C49C3×C4
socleC3×C7×C13C3×C4×C7
prime radicalC3×C7×D13⋊C3C2×C7
cosocleC3×C7×D13C2×C3×C7
LCSG ▷ C3×C13
UCSC1 ◁ C49

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1911

Conjugacy classes & character table

1029 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 144);