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C3×Dic11×C31⋊C3 #27133993

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

Aliases

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

Splittings

derived, HallC11×C31 ⋊ C32×C4
HallC3×C11×C31⋊C3 ⋊ C4
HallC31×Dic11 ⋊ C32
SylowC31 ⋊ C32×Dic11
SylowC11 ⋊ C3×C4×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3D11×C31⋊C3
commutator, hypocenterC11×C31C32×C4
FrattiniC2C3×D11×C31⋊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

546 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12276, 38);