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C53×D165 #31775821

order17490
isoclinismisoclinic class of D165
automorphism?
homologyAbelianization (H1) = C2×C53 · Schur multiplier (H2) = C1

Aliases

direct productC53×D165
unambiguous semidirect productC3⋊(C53×D55)
unambiguous semidirect productC5⋊(C53×D33)
unambiguous semidirect productC11⋊(D15×C53)

Splittings

Fitting, socle, HallC3×C5×C11×C53 ⋊ C2
derived, HallC3×C5×C11 ⋊ C2×C53
HallC5×C11×C53 ⋊ D3
HallC3×C11×C53 ⋊ D5
HallC3×C5×C53 ⋊ D11
HallC11×C53 ⋊ D15
HallC5×C53 ⋊ D33
HallC3×C53 ⋊ D55
HallC5×C11 ⋊ D3×C53
HallC3×C11 ⋊ D5×C53
HallC3×C5 ⋊ D11×C53
SylowC11 ⋊ D15×C53
SylowC5 ⋊ C53×D33
SylowC3 ⋊ C53×D55

Subgroups

subgroupG/H
center, hypercenterC53D165
commutator, cosocle, hypocenterC3×C5×C11C2×C53
FrattiniC1G
Fitting, socleC3×C5×C11×C53C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C53

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8745

Conjugacy classes & character table

4452 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD53×D165, D11×D15×C53, D583⋊D15, …
maximal normal subgroup ofD53×D165, D11×D15×C53, D583⋊D15, …
maximal quotient ofC53×Dic165, C2×C53×D165

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 16);