Finite Group Databasebeta

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A4×C29×C11⋊C5 #34062344

order19140
automorphism?
homologyAbelianization (H1) = C3×C5×C29 · Schur multiplier (H2) = C2

Aliases

direct productA4×C29×C11⋊C5
unambiguous semidirect productC22⋊(C3×C29×C11⋊C5)
unambiguous semidirect productC11⋊(C5×A4×C29)
unambiguous semidirect product(C22×C29)⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×A4)⋊(C5×C29)
unambiguous semidirect product(C22×C11⋊C5)⋊(C3×C29)
unambiguous semidirect product(C11×C29)⋊(C5×A4)
unambiguous semidirect product(C11×A4×C29)⋊C5
unambiguous semidirect product(C22×C29×C11⋊C5)⋊C3

Splittings

Fitting, socle, HallC22×C11×C29 ⋊ C3×C5
derived, HallC22×C11 ⋊ C3×C5×C29
HallC22×C29×C11⋊C5 ⋊ C3
HallC11×A4×C29 ⋊ C5
HallC11×C29 ⋊ C5×A4
HallC22×C11⋊C5 ⋊ C3×C29
HallC11×A4 ⋊ C5×C29
HallC22×C29 ⋊ C3×C11⋊C5
SylowC11 ⋊ C5×A4×C29
SylowC22 ⋊ C3×C29×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC29A4×C11⋊C5
commutator, cosocle, hypocenterC22×C11C3×C5×C29
FrattiniC1G
Fitting, socleC22×C11×C29C3×C5
LCSG ▷ C22×C11
UCSC1 ◁ C29

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1276

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 37);