Finite Group Databasebeta

← Prev (#37567555) Next (#37567557) →

C2×C3×C37×AGL(1,𝔽11) #37567556

order24420
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C37 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C37×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C2×C3×C5×C37)
unambiguous semidirect product(C2×D11)⋊(C3×C5×C37)
unambiguous semidirect product(C11⋊C5)⋊(C22×C3×C37)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×C3×C37)
unambiguous semidirect product(C2×C3×D11)⋊(C5×C37)
unambiguous semidirect product(C2×C3×D11×C37)⋊C5

Splittings

Fitting, socleC2×C3×C11×C37 ⋊ C2×C5
derived, SylowC11 ⋊ C22×C3×C5×C37
HallC3×C37×C11⋊C5 ⋊ C22
HallC2×C3×D11×C37 ⋊ C5
HallC37×C11⋊C5 ⋊ C22×C3
HallC2×D11×C37 ⋊ C3×C5
HallC3×C11×C37 ⋊ C22×C5
HallC11×C37 ⋊ C22×C3×C5
HallC3×C11⋊C5 ⋊ C22×C37
HallC2×C3×D11 ⋊ C5×C37
HallC11⋊C5 ⋊ C22×C3×C37
HallC2×D11 ⋊ C3×C5×C37
HallC3×C11 ⋊ C22×C5×C37

Subgroups

subgroupG/H
center, hypercenterC2×C3×C37AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C22×C3×C5×C37
FrattiniC1G
Fitting, socleC2×C3×C11×C37C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C37

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2442

Conjugacy classes & character table

2442 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 77);