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C11×D735 #30633473

order16170
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D735
unambiguous semidirect productC3⋊(C11×D245)
unambiguous semidirect productC5⋊(C11×D147)
unambiguous semidirect productC49⋊(C11×D15)

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C2
derived, HallC3×C5×C49 ⋊ C2×C11
HallC5×C11×C49 ⋊ D3
HallC3×C11×C49 ⋊ D5
HallC11×C49 ⋊ D15
HallC5×C49 ⋊ D3×C11
HallC3×C5×C11 ⋊ D49
HallC3×C49 ⋊ D5×C11
HallC5×C11 ⋊ D147
SylowC49 ⋊ C11×D15
HallC3×C11 ⋊ D245
HallC3×C5 ⋊ C11×D49
SylowC5 ⋊ C11×D147
SylowC3 ⋊ C11×D245

Subgroups

subgroupG/H
center, hypercenterC11D735
commutator, cosocle, hypocenterC3×C5×C49C2×C11
FrattiniC7C11×D105
FittingC3×C5×C11×C49C2
socleC3×C5×C7×C11D7
LCSG ▷ C3×C5×C49
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

4059 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD11×D735, C11×D15×D49, D539⋊D15, …
maximal normal subgroup ofD11×D735, C11×D15×D49, D539⋊D15, …
maximal quotient ofC11×Dic735, C2×C11×D735

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 18);