Finite Group Databasebeta

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C3×C4×C11×C13⋊C3 #19104173

order5148
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C32×C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C11×C13⋊C3
unambiguous semidirect product(C4×C13)⋊(C32×C11)
unambiguous semidirect product(C3×C4×C13)⋊(C3×C11)
unambiguous semidirect product(C4×C11×C13)⋊C32
unambiguous semidirect product(C3×C4×C11×C13)⋊C3

Splittings

FittingC3×C4×C11×C13 ⋊ C3
derived, SylowC13 ⋊ C32×C4×C11
HallC4×C11×C13 ⋊ C32
HallC11×C13 ⋊ C32×C4
HallC4×C13 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC3×C4×C11C13⋊C3
commutator, hypocenterC13C32×C4×C11
FrattiniC2C2×C3×C11×C13⋊C3
FittingC3×C4×C11×C13C3
socleC2×C3×C11×C13C2×C3
LCSG ▷ C13
UCSC1 ◁ C3×C4×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

924 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C4×C13⋊C3×C11⋊C5, C3×C11×Dic5×C13⋊C3, C3×C4×C5×C11×C13⋊C3, …
maximal normal subgroup ofC3×C4×C13⋊C3×C11⋊C5, C3×C4×C5×C11×C13⋊C3, C3×C4×C7×C11×C13⋊C3
maximal quotient ofC3×C11×Dic5×C13⋊C3, C3×C4×C5×C11×C13⋊C3, C3×C11×AGL(1,𝔽5)×C13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 49);