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C43×D165 #28382001

order14190
isoclinismisoclinic class of D165
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C1

Aliases

direct productC43×D165
unambiguous semidirect productC3⋊(C43×D55)
unambiguous semidirect productC5⋊(C43×D33)
unambiguous semidirect productC11⋊(D15×C43)

Splittings

Fitting, socle, HallC3×C5×C11×C43 ⋊ C2
derived, HallC3×C5×C11 ⋊ C2×C43
HallC5×C11×C43 ⋊ D3
HallC3×C11×C43 ⋊ D5
HallC3×C5×C43 ⋊ D11
HallC11×C43 ⋊ D15
HallC5×C43 ⋊ D33
HallC3×C43 ⋊ D55
HallC5×C11 ⋊ D3×C43
HallC3×C11 ⋊ D5×C43
HallC3×C5 ⋊ D11×C43
SylowC11 ⋊ D15×C43
SylowC5 ⋊ C43×D33
SylowC3 ⋊ C43×D55

Subgroups

subgroupG/H
center, hypercenterC43D165
commutator, cosocle, hypocenterC3×C5×C11C2×C43
FrattiniC1G
Fitting, socleC3×C5×C11×C43C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C43

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7095

Conjugacy classes & character table

3612 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD43×D165, D11×D15×C43, D473⋊D15, …
maximal normal subgroup ofD43×D165, D11×D15×C43, D473⋊D15, …
maximal quotient ofC43×Dic165, C2×C43×D165

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14190, 18);