Finite Group Databasebeta

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C11×(C127⋊C3)⋊C4 #30660918

order16764
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×(C127⋊C3)⋊C4
unambiguous semidirect product(C127⋊C3)⋊(C4×C11)
unambiguous semidirect productDic127⋊(C3×C11)
unambiguous semidirect product(C11×Dic127)⋊C3

Splittings

derived, SylowC127 ⋊ C3×C4×C11
HallC11×Dic127 ⋊ C3
HallC11×C127⋊C3 ⋊ C4
HallC11×C127 ⋊ C3×C4
HallDic127 ⋊ C3×C11
HallC127⋊C3 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11D127⋊C3
commutator, hypocenterC127C3×C4×C11
FrattiniC2C11×D127⋊C3
Fitting, socleC2×C11×C127C2×C3
prime radicalC2×C11×C127⋊C3C2
cosocleC2×C127C2×C3×C11
LCSG ▷ C127
UCSC1 ◁ C2×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5588

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, 10);