Finite Group Databasebeta

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C3×C23×C169⋊C3 #46854329

order34983
automorphism?
homologyAbelianization (H1) = C32×C23 · Schur multiplier (H2) = C3

Aliases

direct productC3×C23×C169⋊C3
unambiguous semidirect productC169⋊(C32×C23)
unambiguous semidirect product(C3×C169)⋊(C3×C23)
unambiguous semidirect product(C23×C169)⋊C32
unambiguous semidirect product(C3×C23×C169)⋊C3

Splittings

FittingC3×C23×C169 ⋊ C3
derived, SylowC169 ⋊ C32×C23
HallC23×C169 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C23C169⋊C3
commutator, cosocle, hypocenterC169C32×C23
FrattiniC13C3×C23×C13⋊C3
FittingC3×C23×C169C3
socleC3×C13×C23C13⋊C3
LCSG ▷ C169
UCSC1 ◁ C3×C23

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11661

Conjugacy classes & character table

4071 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34983, 4);