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C3×C11⋊((C31⋊C3)⋊C4) #27133992

order12276
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11⋊((C31⋊C3)⋊C4)
unambiguous semidirect productC11⋊(C3×(C31⋊C3)⋊C4)
unambiguous semidirect product(C31⋊C3)⋊(C3×Dic11)
unambiguous semidirect productDic341⋊C32
unambiguous semidirect product(C3×Dic341)⋊C3

Splittings

derived, HallC11×C31 ⋊ C32×C4
HallC3×C11×C31⋊C3 ⋊ C4
HallDic341 ⋊ C32
HallC3×C31⋊C3 ⋊ Dic11
SylowC31 ⋊ C32×Dic11
SylowC11 ⋊ C3×(C31⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊(D31⋊C3)
commutator, hypocenterC11×C31C32×C4
FrattiniC2C3×C11⋊(D31⋊C3)
Fitting, socleC2×C3×C11×C31C2×C3
prime radicalC2×C3×C11×C31⋊C3C2
cosocleC2×C11×C31C2×C32
LCSG ▷ C11×C31
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

456 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12276, 37);