Finite Group Databasebeta

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C4×C11×C127⋊C3 #30660910

order16764
isoclinismisoclinic class of C127⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC4×C11×C127⋊C3
unambiguous semidirect product(C4×C127)⋊(C3×C11)
unambiguous semidirect product(C4×C11×C127)⋊C3

Splittings

Fitting, HallC4×C11×C127 ⋊ C3
derived, SylowC127 ⋊ C3×C4×C11
HallC11×C127 ⋊ C3×C4
HallC4×C127 ⋊ C3×C11

Subgroups

subgroupG/H
center, hypercenterC4×C11C127⋊C3
commutator, hypocenterC127C3×C4×C11
FrattiniC2C2×C11×C127⋊C3
FittingC4×C11×C127C3
socleC2×C11×C127C2×C3
prime radicalC2×C11×C127⋊C3C2
cosocleC2×C127C2×C3×C11
LCSG ▷ C127
UCSC1 ◁ C4×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5588

Conjugacy classes & character table

1980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16764, 2);