Finite Group Databasebeta

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C2×C3×C11×C13×C13⋊C3 #45689609

order33462
automorphism?
homologyAbelianization (H1) = C2×C32×C11×C13 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C11×C13×C13⋊C3
unambiguous semidirect product(C2×C13)⋊(C32×C11×C13)
unambiguous semidirect product(C2×C3×C13)⋊(C3×C11×C13)
unambiguous semidirect product(C2×C11×C13)⋊(C32×C13)
unambiguous semidirect product(C2×C3×C11×C13)⋊(C3×C13)

Splittings

Fitting, socleC2×C3×C11×C132 ⋊ C3
derivedC13 ⋊ C2×C32×C11×C13
HallC2×C11×C132 ⋊ C32
HallC11×C132 ⋊ C2×C32
HallC2×C132 ⋊ C32×C11
SylowC132 ⋊ C2×C32×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11×C13C13⋊C3
commutator, cosocle, hypocenterC13C2×C32×C11×C13
FrattiniC1G
Fitting, socleC2×C3×C11×C132C3
LCSG ▷ C13
UCSC1 ◁ C2×C3×C11×C13

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2574

Conjugacy classes & character table

6006 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33462, 117);