Finite Group Databasebeta

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C3×C11×A4×C11⋊C5 #36345173

order21780
automorphism?
homologyAbelianization (H1) = C32×C5×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C11×A4×C11⋊C5
unambiguous semidirect productC22⋊(C32×C11×C11⋊C5)
unambiguous semidirect productC11⋊(C3×C5×C11×A4)
unambiguous semidirect product(C22×C3)⋊(C3×C11×C11⋊C5)
unambiguous semidirect product(C3×C11)⋊(C5×C11×A4)
unambiguous semidirect product(C11×A4)⋊(C3×C5×C11)
unambiguous semidirect product(C22×C11⋊C5)⋊(C32×C11)
unambiguous semidirect product(C3×C11×A4)⋊(C5×C11)
unambiguous semidirect product(C22×C3×C11⋊C5)⋊(C3×C11)
unambiguous semidirect product(C22×C11×C11⋊C5)⋊C32
unambiguous semidirect product(C22×C3×C11×C11⋊C5)⋊C3

Splittings

Fitting, socleC22×C3×C112 ⋊ C3×C5
derivedC22×C11 ⋊ C32×C5×C11
HallC3×C112×A4 ⋊ C5
HallC22×C11×C11⋊C5 ⋊ C32
HallC22×C112 ⋊ C32×C5
SylowC112 ⋊ C3×C5×A4
SylowC22 ⋊ C32×C11×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC3×C11A4×C11⋊C5
commutator, cosocle, hypocenterC22×C11C32×C5×C11
FrattiniC1G
Fitting, socleC22×C3×C112C3×C5
LCSG ▷ C22×C11
UCSC1 ◁ C3×C11

140 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

924 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 522);