Finite Group Databasebeta

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C2×C3×C11×D31⋊C3 #27134019

order12276
isoclinismisoclinic class of D31⋊C3
automorphism?
homologyAbelianization (H1) = C22×C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C11×D31⋊C3
unambiguous semidirect productD31⋊(C2×C32×C11)
unambiguous semidirect product(C31⋊C3)⋊(C22×C3×C11)
unambiguous semidirect product(C2×D31)⋊(C32×C11)
unambiguous semidirect product(C2×C31⋊C3)⋊(C2×C3×C11)
unambiguous semidirect product(C2×C3×D31)⋊(C3×C11)
unambiguous semidirect product(C2×C11×D31)⋊C32
unambiguous semidirect product(C2×C3×C11×D31)⋊C3

Splittings

Fitting, socleC2×C3×C11×C31 ⋊ C2×C3
derived, SylowC31 ⋊ C22×C32×C11
HallC3×C11×C31⋊C3 ⋊ C22
HallC2×C11×D31 ⋊ C32
HallC11×C31 ⋊ C22×C32
HallC3×C31⋊C3 ⋊ C22×C11
HallC2×D31 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D31⋊C3
commutator, cosocle, hypocenterC31C22×C32×C11
FrattiniC1G
Fitting, socleC2×C3×C11×C31C2×C3
LCSG ▷ C31
UCSC1 ◁ C2×C3×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

726 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12276, 64);