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C3×C11×D245 #30633465

order16170
isoclinismisoclinic class of D245
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D245
unambiguous semidirect productC5⋊(C3×C11×D49)

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C2
derived, HallC5×C49 ⋊ C2×C3×C11
HallC5×C11×C49 ⋊ C2×C3
HallC3×C11×C49 ⋊ D5
HallC3×C5×C49 ⋊ C2×C11
HallC11×C49 ⋊ C3×D5
HallC3×C5×C11 ⋊ D49
HallC3×C49 ⋊ D5×C11
HallC5×C11 ⋊ C3×D49
SylowC49 ⋊ C3×D5×C11
HallC3×C5 ⋊ C11×D49
SylowC5 ⋊ C3×C11×D49

Subgroups

subgroupG/H
center, hypercenterC3×C11D245
commutator, cosocle, hypocenterC5×C49C2×C3×C11
FrattiniC7C3×C11×D35
FittingC3×C5×C11×C49C2
socleC3×C5×C7×C11D7
LCSG ▷ C5×C49
UCSC1 ◁ C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

4092 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D11×D245, C3×D5×C11×D49, C3×D55⋊D49, …
maximal normal subgroup ofC3×D11×D245, C3×D5×C11×D49, C3×D55⋊D49, …
maximal quotient ofC3×C11×Dic245, C2×C3×C11×D245

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 10);