Finite Group Databasebeta

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C2×C11×D11×C13⋊C3 #34038422

order18876
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D11×C13⋊C3
unambiguous semidirect productC11⋊(C22×C11×C13⋊C3)
unambiguous semidirect product(C2×C11)⋊(C2×C11×C13⋊C3)
unambiguous semidirect product(C2×C13×D11)⋊(C3×C11)
unambiguous semidirect product(C2×C11×C13×D11)⋊C3

Splittings

Fitting, socleC2×C112×C13 ⋊ C2×C3
derivedC11×C13 ⋊ C22×C3×C11
HallC2×C11×C13×D11 ⋊ C3
HallC112×C13⋊C3 ⋊ C22
HallC112×C13 ⋊ C22×C3
SylowC112 ⋊ C22×C13⋊C3
SylowC13 ⋊ C2×C3×C11×D11

Subgroups

subgroupG/H
center, hypercenterC2×C11D11×C13⋊C3
commutator, cosocle, hypocenterC11×C13C22×C3×C11
FrattiniC1G
Fitting, socleC2×C112×C13C2×C3
LCSG ▷ C11×C13
UCSC1 ◁ C2×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 572

Conjugacy classes & character table

1078 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18876, 104);