Finite Group Databasebeta

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C3×C52×C169⋊C3 #49184602

order38025
automorphism?
homologyAbelianization (H1) = C32×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C52×C169⋊C3
unambiguous semidirect productC169⋊(C32×C52)
unambiguous semidirect product(C3×C169)⋊(C3×C52)
unambiguous semidirect product(C5×C169)⋊(C32×C5)
unambiguous semidirect product(C3×C5×C169)⋊(C3×C5)

Splittings

FittingC3×C52×C169 ⋊ C3
derived, SylowC169 ⋊ C32×C52
HallC52×C169 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C52C169⋊C3
commutator, cosocle, hypocenterC169C32×C52
FrattiniC13C3×C52×C13⋊C3
FittingC3×C52×C169C3
socleC3×C52×C13C13⋊C3
LCSG ▷ C169
UCSC1 ◁ C3×C52

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12675

Conjugacy classes & character table

4425 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38025, 17);