Finite Group Databasebeta

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C2×C3×C5×D37⋊C3 #20269113

order6660
isoclinismisoclinic class of D37⋊C3
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C5×D37⋊C3
unambiguous semidirect productD37⋊(C2×C32×C5)
unambiguous semidirect product(C37⋊C3)⋊(C22×C3×C5)
unambiguous semidirect product(C2×D37)⋊(C32×C5)
unambiguous semidirect product(C2×C37⋊C3)⋊(C2×C3×C5)
unambiguous semidirect product(C2×C3×D37)⋊(C3×C5)
unambiguous semidirect product(C2×C5×D37)⋊C32
unambiguous semidirect product(C2×C3×C5×D37)⋊C3

Splittings

Fitting, socleC2×C3×C5×C37 ⋊ C2×C3
derived, SylowC37 ⋊ C22×C32×C5
HallC3×C5×C37⋊C3 ⋊ C22
HallC2×C5×D37 ⋊ C32
HallC3×C37⋊C3 ⋊ C22×C5
HallC5×C37 ⋊ C22×C32
HallC2×D37 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D37⋊C3
commutator, hypocenterC37C22×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C37C2×C3
LCSG ▷ C37
UCSC1 ◁ C2×C3×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

360 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×C25×D37⋊C3, C3×C5×D5×D37⋊C3, C2×C3×C52×D37⋊C3, …
maximal normal subgroup ofC2×C3×C25×D37⋊C3, C2×C3×C52×D37⋊C3
maximal quotient ofC2×C3×C25×D37⋊C3, C3×C5×D5×D37⋊C3, C2×C3×C52×D37⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6660, 110);