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C3×C11×C22⋊(C13⋊C3) #19104240

order5148
isoclinismisoclinic class of C22⋊(C13⋊C3)
automorphism?
homologyAbelianization (H1) = C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C11×C22⋊(C13⋊C3)
unambiguous semidirect product(C22×C3)⋊(C11×C13⋊C3)
unambiguous semidirect product(C3×C13)⋊(C11×A4)
unambiguous semidirect product(C22×C3×C11)⋊(C13⋊C3)
unambiguous semidirect product(C3×C11×C13)⋊A4

Splittings

Fitting, socleC22×C3×C11×C13 ⋊ C3
derived, HallC22×C13 ⋊ C32×C11
HallC22×C11×C13 ⋊ C32
HallC11×C13 ⋊ C3×A4
HallC22×C11 ⋊ C3×C13⋊C3
SylowC13 ⋊ C3×C11×A4
SylowC22 ⋊ C3×C11×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C11C22⋊(C13⋊C3)
commutator, hypocenterC22×C13C32×C11
FrattiniC1G
Fitting, socleC22×C3×C11×C13C3
LCSG ▷ C22×C13
UCSC1 ◁ C3×C11

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11⋊C5×C22⋊(C13⋊C3), C3×C5×C11×C22⋊(C13⋊C3), C11×ΓL(1,𝔽8)×C22⋊(C13⋊C3), …
maximal normal subgroup ofC3×C11⋊C5×C22⋊(C13⋊C3), C3×C5×C11×C22⋊(C13⋊C3), C3×C7×C11×C22⋊(C13⋊C3)
maximal quotient ofC3×C5×C11×C22⋊(C13⋊C3), C11×ΓL(1,𝔽8)×C22⋊(C13⋊C3), C3×C7×C11×C22⋊(C13⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 116);