Finite Group Databasebeta

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C3×C49×D55 #30633464

order16170
isoclinismisoclinic class of D55
automorphism?
homologyAbelianization (H1) = C2×C3×C49 · Schur multiplier (H2) = C1

Aliases

direct productC3×C49×D55
unambiguous semidirect productC5⋊(C3×D11×C49)
unambiguous semidirect productC11⋊(C3×D5×C49)

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C2
derived, HallC5×C11 ⋊ C2×C3×C49
HallC5×C11×C49 ⋊ C2×C3
HallC3×C11×C49 ⋊ D5
HallC3×C5×C49 ⋊ D11
HallC11×C49 ⋊ C3×D5
HallC5×C49 ⋊ C3×D11
HallC3×C5×C11 ⋊ C2×C49
HallC3×C11 ⋊ D5×C49
HallC3×C5 ⋊ D11×C49
SylowC11 ⋊ C3×D5×C49
SylowC5 ⋊ C3×D11×C49

Subgroups

subgroupG/H
center, hypercenterC3×C49D55
commutator, hypocenterC5×C11C2×C3×C49
FrattiniC7C3×C7×D55
FittingC3×C5×C11×C49C2
socleC3×C5×C7×C11C2×C7
prime radicalC3×C7×D55C7
cosocleC5×C7×C11C2×C3×C7
LCSG ▷ C5×C11
UCSC1 ◁ C3×C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

4263 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D5×D11×C49, C3×D49×D55, C3×D55⋊D49, …
maximal normal subgroup ofC3×D5×D11×C49, C3×D49×D55, C3×D55⋊D49, …
maximal quotient ofC3×C49×Dic55, C2×C3×C49×D55

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 9);