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C3×C3⋊#13049907 #26043293

order11700
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊#13049907
unambiguous semidirect productC3⋊(C3×#13049907)

Splittings

Fitting, HallC32×C13×C25 ⋊ C4
derivedC3×C13×C25 ⋊ C3×C4
HallC13×C25 ⋊ C3×Dic3
HallC32×C25 ⋊ #261
HallC32×C13 ⋊ #1035
SylowC25 ⋊ C3×C3⋊#261
SylowC13 ⋊ C3×C3⋊#1035
SylowC32 ⋊ #13049907

Subgroups

subgroupG/H
center, hypercenterC3C3⋊#13049907
commutator, hypocenterC3×C13×C25C3×C4
FrattiniC5C3×C3⋊#63121
FittingC32×C13×C25C4
socleC32×C5×C13AGL(1,𝔽5)
prime radicalC32×D325C2
cosocleC3×D325C2×C3
LCSG ▷ C3×C13×C25
UCSC1 ◁ C3

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

747 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 140);