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C49×D165 #30633472

order16170
isoclinismisoclinic class of D165
automorphism?
homologyAbelianization (H1) = C2×C49 · Schur multiplier (H2) = C1

Aliases

direct productC49×D165
unambiguous semidirect productC3⋊(C49×D55)
unambiguous semidirect productC5⋊(C49×D33)
unambiguous semidirect productC11⋊(D15×C49)

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C2
derived, HallC3×C5×C11 ⋊ C2×C49
HallC5×C11×C49 ⋊ D3
HallC3×C11×C49 ⋊ D5
HallC3×C5×C49 ⋊ D11
HallC11×C49 ⋊ D15
HallC5×C49 ⋊ D33
HallC3×C49 ⋊ D55
HallC5×C11 ⋊ D3×C49
HallC3×C11 ⋊ D5×C49
HallC3×C5 ⋊ D11×C49
SylowC11 ⋊ D15×C49
SylowC5 ⋊ C49×D33
SylowC3 ⋊ C49×D55

Subgroups

subgroupG/H
center, hypercenterC49D165
commutator, hypocenterC3×C5×C11C2×C49
FrattiniC7C7×D165
FittingC3×C5×C11×C49C2
socle, cosocleC3×C5×C7×C11C2×C7
prime radicalC7×D165C7
LCSG ▷ C3×C5×C11
UCSC1 ◁ C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

4116 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD11×D15×C49, D49×D165, D539⋊D15, …
maximal normal subgroup ofD11×D15×C49, D49×D165, D539⋊D15, …
maximal quotient ofC49×Dic165, C2×C49×D165

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 17);