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C2×C3×C37⋊AGL(1,𝔽11) #37567557

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

Aliases

direct productC2×C3×C37⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C11⋊C5)⋊(C3×D37)
unambiguous semidirect product(C2×C3×D407)⋊C5

Splittings

Fitting, socleC2×C3×C11×C37 ⋊ C2×C5
derived, HallC11×C37 ⋊ C22×C3×C5
HallC3×C37×C11⋊C5 ⋊ C22
HallC2×C3×D407 ⋊ C5
HallC37×C11⋊C5 ⋊ C22×C3
HallC2×D407 ⋊ C3×C5
HallC3×C11×C37 ⋊ C22×C5
HallC3×C11⋊C5 ⋊ C2×D37
HallC3×C37 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×C3×D37
SylowC37 ⋊ C2×C3×AGL(1,𝔽11)
HallC3×C11 ⋊ C2×C5×D37
SylowC11 ⋊ C2×C3×C5×D37

Subgroups

subgroupG/H
center, hypercenterC2×C3C37⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C37C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C37C2×C5
LCSG ▷ C11×C37
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2442

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 78);