Finite Group Databasebeta

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C2×C5×C11×AGL(1,𝔽19) #49178562

order37620
automorphism?
homologyAbelianization (H1) = C22×C5×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C11×AGL(1,𝔽19)
unambiguous semidirect product#4296⋊(C22×C5×C11)
unambiguous semidirect product(C2×#4296)⋊(C2×C5×C11)

Splittings

Fitting, socleC2×C5×C11×C19 ⋊ C2×C9
derived, SylowC19 ⋊ C22×C5×C9×C11
HallC5×C11×#4296 ⋊ C22
HallC2×C5×C11×D19 ⋊ C9
HallC11×#4296 ⋊ C22×C5
HallC5×C11×C19 ⋊ C22×C9
HallC5×#4296 ⋊ C22×C11
HallC2×C11×D19 ⋊ C5×C9
HallC2×C5×D19 ⋊ C9×C11
HallC11×C19 ⋊ C22×C5×C9
Hall#4296 ⋊ C22×C5×C11
HallC5×C19 ⋊ C22×C9×C11
HallC2×D19 ⋊ C5×C9×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11AGL(1,𝔽19)
commutator, hypocenterC19C22×C5×C9×C11
FrattiniC1G
Fitting, socleC2×C5×C11×C19C2×C9
prime radicalC2×C5×C11×D19⋊C3C3
cosocleC19⋊C3C22×C3×C5×C11
LCSG ▷ C19
UCSC1 ◁ C2×C5×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2090

Conjugacy classes & character table

2090 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 271);