Finite Group Databasebeta

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C3×D5×D169⋊C3 #44477491

order30420
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×D5×D169⋊C3
unambiguous semidirect productD169⋊(C32×D5)
unambiguous semidirect product(D5×D169)⋊C32
unambiguous semidirect product(C5×D169⋊C3)⋊(C2×C3)
unambiguous semidirect product(D5×C169⋊C3)⋊(C2×C3)
unambiguous semidirect product(C5⋊(D169⋊C3))⋊(C2×C3)
unambiguous semidirect product(C3×D5×D169)⋊C3

Splittings

FittingC3×C5×C169 ⋊ C22×C3
derived, HallC5×C169 ⋊ C22×C32
HallC3×C5×C169⋊C3 ⋊ C22
HallD5×D169 ⋊ C32
HallC3×C169⋊C3 ⋊ C2×D5
SylowC169 ⋊ C2×C32×D5
SylowC5 ⋊ C2×C3×D169⋊C3

Subgroups

subgroupG/H
center, hypercenterC3D5×D169⋊C3
commutator, cosocle, hypocenterC5×C169C22×C32
FrattiniC13C3×D5×D13⋊C3
FittingC3×C5×C169C22×C3
socleC3×C5×C13C2×D13⋊C3
LCSG ▷ C5×C169
UCSC1 ◁ C3

180 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2535

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 80);