Finite Group Databasebeta

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C2×C11×D127⋊C3 #30660923

order16764
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D127⋊C3
unambiguous semidirect productD127⋊(C2×C3×C11)
unambiguous semidirect product(C127⋊C3)⋊(C22×C11)
unambiguous semidirect product(C2×D127)⋊(C3×C11)
unambiguous semidirect product(C2×C127⋊C3)⋊(C2×C11)
unambiguous semidirect product(C2×C11×D127)⋊C3

Splittings

Fitting, socleC2×C11×C127 ⋊ C2×C3
derived, SylowC127 ⋊ C22×C3×C11
HallC2×C11×D127 ⋊ C3
HallC11×C127⋊C3 ⋊ C22
HallC11×C127 ⋊ C22×C3
HallC2×D127 ⋊ C3×C11
HallC127⋊C3 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11D127⋊C3
commutator, cosocle, hypocenterC127C22×C3×C11
FrattiniC1G
Fitting, socleC2×C11×C127C2×C3
LCSG ▷ C127
UCSC1 ◁ C2×C11

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2794

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16764, 15);