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C3×C11×C22⋊(C19⋊C3) #21419064

order7524
isoclinismisoclinic class of C22⋊(C19⋊C3)
automorphism?
homologyAbelianization (H1) = C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C11×C22⋊(C19⋊C3)
unambiguous semidirect product(C22×C3)⋊(C11×C19⋊C3)
unambiguous semidirect product(C3×C19)⋊(C11×A4)
unambiguous semidirect product(C22×C3×C11)⋊(C19⋊C3)
unambiguous semidirect product(C3×C11×C19)⋊A4

Splittings

Fitting, socleC22×C3×C11×C19 ⋊ C3
derived, HallC22×C19 ⋊ C32×C11
HallC22×C11×C19 ⋊ C32
HallC11×C19 ⋊ C3×A4
HallC22×C11 ⋊ C3×C19⋊C3
SylowC19 ⋊ C3×C11×A4
SylowC22 ⋊ C3×C11×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C11C22⋊(C19⋊C3)
commutator, hypocenterC22×C19C32×C11
FrattiniC1G
Fitting, socleC22×C3×C11×C19C3
LCSG ▷ C22×C19
UCSC1 ◁ C3×C11

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

924 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11⋊C5×C22⋊(C19⋊C3), C3×C5×C11×C22⋊(C19⋊C3)
maximal normal subgroup ofC3×C11⋊C5×C22⋊(C19⋊C3), C3×C5×C11×C22⋊(C19⋊C3)
maximal quotient ofC3×C5×C11×C22⋊(C19⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7524, 108);