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C2×C37×C3⋊AGL(1,𝔽11) #37567559

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

Aliases

direct productC2×C37×C3⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C3)⋊(C37×AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(D3×C37)
unambiguous semidirect product(C2×D33)⋊(C5×C37)
unambiguous semidirect product(C2×C37×D33)⋊C5

Splittings

Fitting, socleC2×C3×C11×C37 ⋊ C2×C5
derived, HallC3×C11 ⋊ C22×C5×C37
HallC3×C37×C11⋊C5 ⋊ C22
HallC2×C37×D33 ⋊ C5
HallC37×C11⋊C5 ⋊ C2×D3
HallC3×C11×C37 ⋊ C22×C5
HallC11×C37 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C22×C37
HallC2×D33 ⋊ 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, hypercenterC2×C37C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C22×C5×C37
FrattiniC1G
Fitting, socleC2×C3×C11×C37C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C2×C37

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2442

Conjugacy classes & character table

1332 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 80);