Finite Group Databasebeta

← Prev (#37563514) Next (#37563516) →

C11×A4×C61⋊C3 #37563515

order24156
automorphism?
homologyAbelianization (H1) = C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC11×A4×C61⋊C3
unambiguous semidirect product(C22×C61⋊C3)⋊(C3×C11)
unambiguous semidirect product(A4×C61)⋊(C3×C11)
unambiguous semidirect product(C22⋊(C61⋊C3))⋊(C3×C11)
unambiguous semidirect product(C11×C22⋊(C61⋊C3))⋊C3
unambiguous semidirect product(C11×A4×C61)⋊C3
unambiguous semidirect product(C22×C11×C61⋊C3)⋊C3

Splittings

Fitting, socle, HallC22×C11×C61 ⋊ C32
derived, HallC22×C61 ⋊ C32×C11
HallC11×C61 ⋊ C3×A4
SylowC61 ⋊ C3×C11×A4
HallC22×C11 ⋊ C3×C61⋊C3
SylowC22 ⋊ C3×C11×C61⋊C3

Subgroups

subgroupG/H
center, hypercenterC11A4×C61⋊C3
commutator, cosocle, hypocenterC22×C61C32×C11
FrattiniC1G
Fitting, socleC22×C11×C61C32
LCSG ▷ C22×C61
UCSC1 ◁ C11

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2684

Conjugacy classes & character table

1012 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24156, 73);