Finite Group Databasebeta

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C7×C11×A4×C13⋊C3 #49114808

order36036
automorphism?
homologyAbelianization (H1) = C32×C7×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC7×C11×A4×C13⋊C3
unambiguous semidirect product(C22×C13⋊C3)⋊(C3×C7×C11)
unambiguous semidirect product(A4×C13)⋊(C3×C7×C11)
unambiguous semidirect product(C22⋊(C13⋊C3))⋊(C3×C7×C11)
unambiguous semidirect product(C22×C11×C13⋊C3)⋊(C3×C7)
unambiguous semidirect product(C11×A4×C13)⋊(C3×C7)
unambiguous semidirect product(C11×C22⋊(C13⋊C3))⋊(C3×C7)

Splittings

Fitting, socle, HallC22×C7×C11×C13 ⋊ C32
derived, HallC22×C13 ⋊ C32×C7×C11
HallC7×C11×C13 ⋊ C3×A4
HallC22×C11×C13 ⋊ C32×C7
HallC22×C7×C13 ⋊ C32×C11
HallC22×C7×C11 ⋊ C3×C13⋊C3
HallC11×C13 ⋊ C3×C7×A4
HallC7×C13 ⋊ C3×C11×A4
HallC22×C11 ⋊ C3×C7×C13⋊C3
HallC22×C7 ⋊ C3×C11×C13⋊C3
SylowC13 ⋊ C3×C7×C11×A4
SylowC22 ⋊ C3×C7×C11×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC7×C11A4×C13⋊C3
commutator, cosocle, hypocenterC22×C13C32×C7×C11
FrattiniC1G
Fitting, socleC22×C7×C11×C13C32
LCSG ▷ C22×C13
UCSC1 ◁ C7×C11

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4004

Conjugacy classes & character table

2156 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 476);