Finite Group Databasebeta

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C3×C11×(C19⋊C3)⋊AGL(1,𝔽5) #49178573

order37620
automorphism?
homologyAbelianization (H1) = C32×C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11×(C19⋊C3)⋊AGL(1,𝔽5)
unambiguous semidirect product(C19⋊C3)⋊(C3×C11×AGL(1,𝔽5))
unambiguous semidirect product(C19⋊AGL(1,𝔽5))⋊(C32×C11)
unambiguous semidirect product(C3×C19⋊AGL(1,𝔽5))⋊(C3×C11)
unambiguous semidirect product(C11×C19⋊AGL(1,𝔽5))⋊C32
unambiguous semidirect product(C3×C11×C19⋊AGL(1,𝔽5))⋊C3

Splittings

Fitting, socleC3×C5×C11×C19 ⋊ C3×C4
derived, HallC5×C19 ⋊ C32×C4×C11
HallC3×C5×C11×C19⋊C3 ⋊ C4
HallC11×C19⋊AGL(1,𝔽5) ⋊ C32
HallC3×C11×C19⋊C3 ⋊ AGL(1,𝔽5)
HallC5×C11×C19 ⋊ C32×C4
HallC3×C5×C19⋊C3 ⋊ C4×C11
HallC19⋊AGL(1,𝔽5) ⋊ C32×C11
HallC11×C19 ⋊ C32×AGL(1,𝔽5)
HallC3×C19⋊C3 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ C3×(C19⋊C3)⋊C4
SylowC19 ⋊ C32×C11×AGL(1,𝔽5)
SylowC5 ⋊ C3×C11×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC3×C11(C19⋊C3)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C19C32×C4×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C19C3×C4
prime radicalC3×D5×C11×C19⋊C3C2
cosocleD5×C19C2×C32×C11
LCSG ▷ C5×C19
UCSC1 ◁ C3×C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 282);