Finite Group Databasebeta

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D3×C37×AGL(1,𝔽11) #37567528

order24420
automorphism?
homologyAbelianization (H1) = C22×C5×C37 · Schur multiplier (H2) = C2

Aliases

direct productD3×C37×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×D3×C37)
unambiguous semidirect product(D3×D11)⋊(C5×C37)
unambiguous semidirect product(C3×AGL(1,𝔽11))⋊(C2×C37)
unambiguous semidirect product(D3×C11⋊C5)⋊(C2×C37)
unambiguous semidirect product(C3⋊AGL(1,𝔽11))⋊(C2×C37)
unambiguous semidirect product(D3×D11×C37)⋊C5

Splittings

Fitting, socle, HallC3×C11×C37 ⋊ C22×C5
derived, HallC3×C11 ⋊ C22×C5×C37
HallC3×C37×C11⋊C5 ⋊ C22
HallD3×D11×C37 ⋊ C5
HallC37×C11⋊C5 ⋊ C2×D3
HallC11×C37 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C22×C37
HallD3×D11 ⋊ C5×C37
HallC3×C37 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×D3×C37
SylowC11 ⋊ C2×C5×D3×C37
SylowC3 ⋊ C2×C37×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC37D3×AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C22×C5×C37
FrattiniC1G
Fitting, socleC3×C11×C37C22×C5
LCSG ▷ C3×C11
UCSC1 ◁ C37

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1221

Conjugacy classes & character table

1221 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 49);