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C2×C3×C5×C169⋊C3 #29503558

order15210
isoclinismisoclinic class of C169⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C5×C169⋊C3
unambiguous semidirect product(C2×C169)⋊(C32×C5)
unambiguous semidirect product(C2×C3×C169)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C169)⋊C32
unambiguous semidirect product(C2×C3×C5×C169)⋊C3

Splittings

FittingC2×C3×C5×C169 ⋊ C3
derived, SylowC169 ⋊ C2×C32×C5
HallC2×C5×C169 ⋊ C32
HallC5×C169 ⋊ C2×C32
HallC2×C169 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C169⋊C3
commutator, cosocle, hypocenterC169C2×C32×C5
FrattiniC13C2×C3×C5×C13⋊C3
FittingC2×C3×C5×C169C3
socleC2×C3×C5×C13C13⋊C3
LCSG ▷ C169
UCSC1 ◁ C2×C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5070

Conjugacy classes & character table

1770 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×Dic169⋊C3, C3×Dic5×C169⋊C3, C3×Dic845⋊C3, …
maximal normal subgroup ofC3×C5×Dic169⋊C3, C3×Dic5×C169⋊C3, C3×Dic845⋊C3, …
maximal quotient ofC3×C4×C5×C169⋊C3, C22×C3×C5×C169⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15210, 21);