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C2×C5×C11⋊AGL(1,𝔽19) #49178563

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

Aliases

direct productC2×C5×C11⋊AGL(1,𝔽19)
unambiguous semidirect product(C2×#4296)⋊(C5×D11)

Splittings

Fitting, socleC2×C5×C11×C19 ⋊ C2×C9
derived, HallC11×C19 ⋊ C22×C5×C9
HallC5×C11×#4296 ⋊ C22
HallC2×C5×D209 ⋊ C9
HallC11×#4296 ⋊ C22×C5
HallC5×C11×C19 ⋊ C22×C9
HallC5×#4296 ⋊ C2×D11
HallC2×D209 ⋊ C5×C9
Hall#4296 ⋊ C2×C5×D11
HallC5×C19 ⋊ C2×C9×D11
HallC5×C11 ⋊ C2×AGL(1,𝔽19)
SylowC19 ⋊ C2×C5×C9×D11
SylowC11 ⋊ C2×C5×AGL(1,𝔽19)

Subgroups

subgroupG/H
center, hypercenterC2×C5C11⋊AGL(1,𝔽19)
commutator, hypocenterC11×C19C22×C5×C9
FrattiniC1G
Fitting, socleC2×C5×C11×C19C2×C9
prime radicalC2×C5×C11⋊(D19⋊C3)C3
cosocleC11×C19⋊C3C22×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C2×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2090

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 272);