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C3×C5⋊(D37⋊C3) #16809679

order3330
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5⋊(D37⋊C3)
unambiguous semidirect productC5⋊(C3×D37⋊C3)
unambiguous semidirect product(C37⋊C3)⋊(C3×D5)
unambiguous semidirect productD185⋊C32
unambiguous semidirect product(C3×D185)⋊C3

Splittings

Fitting, socleC3×C5×C37 ⋊ C2×C3
derived, HallC5×C37 ⋊ C2×C32
HallC3×C5×C37⋊C3 ⋊ C2
HallD185 ⋊ C32
HallC3×C37⋊C3 ⋊ D5
SylowC37 ⋊ C32×D5
SylowC5 ⋊ C3×D37⋊C3

Subgroups

subgroupG/H
center, hypercenterC3C5⋊(D37⋊C3)
commutator, cosocle, hypocenterC5×C37C2×C32
FrattiniC1G
Fitting, socleC3×C5×C37C2×C3
LCSG ▷ C5×C37
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 555

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C25⋊(D37⋊C3), C3×C5×C5⋊(D37⋊C3), C3×C5⋊(C5⋊(D37⋊C3)), …
maximal normal subgroup ofC3×C5×C5⋊(D37⋊C3), C3×C7×C5⋊(D37⋊C3), C3×C11×C5⋊(D37⋊C3)
maximal quotient ofC3×C25⋊(D37⋊C3), C3×C5×C5⋊(D37⋊C3), C3×C5⋊(C5⋊(D37⋊C3)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3330, 19);