Finite Group Databasebeta

← Prev (#34088879) Next (#34088881) →

C11×A4×C149 #34088880

order19668
automorphism?
homologyAbelianization (H1) = C3×C11×C149 · Schur multiplier (H2) = C2

Aliases

direct productC11×A4×C149
unambiguous semidirect productC22⋊(C3×C11×C149)
unambiguous semidirect product(C22×C11)⋊(C3×C149)
unambiguous semidirect product(C22×C149)⋊(C3×C11)
unambiguous semidirect product(C22×C11×C149)⋊C3

Splittings

Fitting, socle, HallC22×C11×C149 ⋊ C3
derived, SylowC22 ⋊ C3×C11×C149
HallC22×C149 ⋊ C3×C11
HallC22×C11 ⋊ C3×C149

Subgroups

subgroupG/H
center, hypercenterC11×C149A4
commutator, cosocle, hypocenterC22C3×C11×C149
FrattiniC1G
Fitting, socleC22×C11×C149C3
LCSG ▷ C22
UCSC1 ◁ C11×C149

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6556

Conjugacy classes & character table

6556 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19668, 21);