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C5×C11×D37⋊C3 #27131972

order12210
isoclinismisoclinic class of D37⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D37⋊C3
unambiguous semidirect productD37⋊(C3×C5×C11)
unambiguous semidirect product(C37⋊C3)⋊(C2×C5×C11)
unambiguous semidirect product(C5×D37)⋊(C3×C11)
unambiguous semidirect product(C5×C11×D37)⋊C3

Splittings

Fitting, socle, HallC5×C11×C37 ⋊ C2×C3
derived, SylowC37 ⋊ C2×C3×C5×C11
HallC5×C11×C37⋊C3 ⋊ C2
HallC5×C11×D37 ⋊ C3
HallC11×C37⋊C3 ⋊ C2×C5
HallC11×D37 ⋊ C3×C5
HallC5×C37⋊C3 ⋊ C2×C11
HallC11×C37 ⋊ C2×C3×C5
HallC5×D37 ⋊ C3×C11
HallC5×C37 ⋊ C2×C3×C11
HallC37⋊C3 ⋊ C2×C5×C11
HallD37 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11D37⋊C3
commutator, cosocle, hypocenterC37C2×C3×C5×C11
FrattiniC1G
Fitting, socleC5×C11×C37C2×C3
LCSG ▷ C37
UCSC1 ◁ C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C11×#3866⋊C3, C5×C11⋊(#3866⋊C3), C5×D11×D37⋊C3, …
maximal normal subgroup ofC5×C11×#3866⋊C3, C5×C11⋊(#3866⋊C3), C5×D11×D37⋊C3, …
maximal quotient ofC5×C11×Dic37⋊C3, C2×C5×C11×D37⋊C3, C5×C11×#66524⋊C2, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12210, 27);