Finite Group Databasebeta

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C13×D11×AGL(1,𝔽11) #44538166

order31460
automorphism?
homologyAbelianization (H1) = C22×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×D11×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×C13×D11)
unambiguous semidirect product(C11×AGL(1,𝔽11))⋊(C2×C13)
unambiguous semidirect product((C11⋊C5)⋊D11)⋊(C2×C13)
unambiguous semidirect product(D11×C11⋊C5)⋊(C2×C13)

Splittings

Fitting, socle, HallC112×C13 ⋊ C22×C5
derived, SylowC112 ⋊ C22×C5×C13
HallC11×C13×C11⋊C5 ⋊ C22
HallC13×D112 ⋊ C5
HallC11×C11⋊C5 ⋊ C22×C13
HallD112 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC13D11×AGL(1,𝔽11)
commutator, cosocle, hypocenterC112C22×C5×C13
FrattiniC1G
Fitting, socleC112×C13C22×C5
LCSG ▷ C112
UCSC1 ◁ C13

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1430

Conjugacy classes & character table

1001 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 106);