Finite Group Databasebeta

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C5×C49×D33 #30633468

order16170
isoclinismisoclinic class of D33
automorphism?
homologyAbelianization (H1) = C2×C5×C49 · Schur multiplier (H2) = C1

Aliases

direct productC5×C49×D33
unambiguous semidirect productC3⋊(C5×D11×C49)

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C2
derived, HallC3×C11 ⋊ C2×C5×C49
HallC5×C11×C49 ⋊ D3
HallC3×C11×C49 ⋊ C2×C5
HallC3×C5×C49 ⋊ D11
HallC11×C49 ⋊ C5×D3
HallC3×C5×C11 ⋊ C2×C49
HallC3×C49 ⋊ C5×D11
HallC5×C11 ⋊ D3×C49
HallC3×C5 ⋊ D11×C49
SylowC11 ⋊ C5×D3×C49
SylowC3 ⋊ C5×D11×C49

Subgroups

subgroupG/H
center, hypercenterC5×C49D33
commutator, hypocenterC3×C11C2×C5×C49
FrattiniC7C5×C7×D33
FittingC3×C5×C11×C49C2
socleC3×C5×C7×C11C2×C7
prime radicalC5×C7×D33C7
cosocleC3×C7×C11C2×C5×C7
LCSG ▷ C3×C11
UCSC1 ◁ C5×C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

4410 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×D11×C49, C5×D33×D49, C5×D33⋊D49, …
maximal normal subgroup ofC5×D3×D11×C49, C5×D33×D49, C5×D33⋊D49, …
maximal quotient ofC5×C49×Dic33, C2×C5×C49×D33

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 13);