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C31×(C19⋊C3)⋊AGL(1,𝔽5) #47977640

order35340
automorphism?
homologyAbelianization (H1) = C3×C4×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×(C19⋊C3)⋊AGL(1,𝔽5)
unambiguous semidirect product(C19⋊C3)⋊(AGL(1,𝔽5)×C31)
unambiguous semidirect product(C19⋊AGL(1,𝔽5))⋊(C3×C31)

Splittings

Fitting, socle, HallC5×C19×C31 ⋊ C3×C4
derived, HallC5×C19 ⋊ C3×C4×C31
HallC31×C19⋊AGL(1,𝔽5) ⋊ C3
HallC5×C31×C19⋊C3 ⋊ C4
HallC31×C19⋊C3 ⋊ AGL(1,𝔽5)
HallC19×C31 ⋊ C3×AGL(1,𝔽5)
HallC19⋊AGL(1,𝔽5) ⋊ C3×C31
HallC5×C19⋊C3 ⋊ C4×C31
HallC5×C31 ⋊ (C19⋊C3)⋊C4
HallC19⋊C3 ⋊ AGL(1,𝔽5)×C31
SylowC19 ⋊ C3×AGL(1,𝔽5)×C31
SylowC5 ⋊ C31×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC31(C19⋊C3)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C19C3×C4×C31
FrattiniC1G
Fitting, socleC5×C19×C31C3×C4
prime radicalD5×C31×C19⋊C3C2
cosocleD5×C19C2×C3×C31
LCSG ▷ C5×C19
UCSC1 ◁ C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2945

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 112);