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C2×C9×C19⋊AGL(1,𝔽11) #49178355

order37620
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×C19⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C11⋊C5)⋊(C9×D19)
unambiguous semidirect product(C2×C9×D209)⋊C5

Splittings

FittingC2×C9×C11×C19 ⋊ C2×C5
derived, HallC11×C19 ⋊ C22×C5×C9
HallC9×C19×C11⋊C5 ⋊ C22
HallC2×C9×D209 ⋊ C5
HallC9×C11×C19 ⋊ C22×C5
HallC19×C11⋊C5 ⋊ C22×C9
HallC2×D209 ⋊ C5×C9
HallC9×C11⋊C5 ⋊ C2×D19
HallC9×C19 ⋊ C2×AGL(1,𝔽11)
HallC9×C11 ⋊ C2×C5×D19
HallC11⋊C5 ⋊ C2×C9×D19
SylowC19 ⋊ C2×C9×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×C9×D19

Subgroups

subgroupG/H
center, hypercenterC2×C9C19⋊AGL(1,𝔽11)
commutator, hypocenterC11×C19C22×C5×C9
FrattiniC3C2×C3×C19⋊AGL(1,𝔽11)
FittingC2×C9×C11×C19C2×C5
socleC2×C3×C11×C19C2×C3×C5
prime radicalC2×C3×C19⋊AGL(1,𝔽11)C3
cosocleC3×C11×C19C22×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C2×C9

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3762

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(37620, 64);