Finite Group Databasebeta

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AGL(1,𝔽11)×D37⋊C3 #37567518

order24420
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productAGL(1,𝔽11)×D37⋊C3
unambiguous semidirect productD11⋊(C5×D37⋊C3)
unambiguous semidirect productD37⋊(C3×AGL(1,𝔽11))
unambiguous semidirect product(D11×D37⋊C3)⋊C5
unambiguous semidirect product(D37×AGL(1,𝔽11))⋊C3
unambiguous semidirect product(C11⋊C5×D37⋊C3)⋊C2
unambiguous semidirect product(AGL(1,𝔽11)×C37⋊C3)⋊C2
unambiguous semidirect product((C11⋊C5)⋊(D37⋊C3))⋊C2

Splittings

Fitting, socle, derived, HallC11×C37 ⋊ C22×C3×C5
HallD37×AGL(1,𝔽11) ⋊ C3
HallC11⋊C5×C37⋊C3 ⋊ C22
HallD11×D37⋊C3 ⋊ C5
HallC37×C11⋊C5 ⋊ C22×C3
HallD11×D37 ⋊ C3×C5
HallC11×C37⋊C3 ⋊ C22×C5
HallC37⋊C3 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×D37⋊C3
SylowC37 ⋊ C2×C3×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D37⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C37C22×C3×C5
LCSG ▷ C11×C37
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 407

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 39);