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C11×D13×AGL(1,𝔽11) #44538163

order31460
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D13×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×C11×D13)
unambiguous semidirect product(D11×D13)⋊(C5×C11)
unambiguous semidirect product(D13×C11⋊C5)⋊(C2×C11)
unambiguous semidirect product(C13×AGL(1,𝔽11))⋊(C2×C11)
unambiguous semidirect product(C13⋊AGL(1,𝔽11))⋊(C2×C11)

Splittings

Fitting, socle, HallC112×C13 ⋊ C22×C5
derivedC11×C13 ⋊ C22×C5×C11
HallC11×C13×C11⋊C5 ⋊ C22
HallC11×D11×D13 ⋊ C5
HallC11×C11⋊C5 ⋊ C2×D13
SylowC112 ⋊ C2×C5×D13
SylowC13 ⋊ C2×C11×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC11D13×AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C13C22×C5×C11
FrattiniC1G
Fitting, socleC112×C13C22×C5
LCSG ▷ C11×C13
UCSC1 ◁ C11

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1430

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 103);