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C3⋊(C3⋊(C7⋊(C19⋊AGL(1,𝔽5)))) #37561597

order23940
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊(C3⋊(C7⋊(C19⋊AGL(1,𝔽5))))
unambiguous semidirect productC7⋊(C3⋊(C3⋊(C19⋊AGL(1,𝔽5))))
unambiguous semidirect productC19⋊(C3⋊(C3⋊(C7⋊AGL(1,𝔽5))))

Splittings

Fitting, socle, derived, HallC32×C5×C7×C19 ⋊ C4
HallC32×C7×C19 ⋊ AGL(1,𝔽5)
HallC32×C5×C19 ⋊ Dic7
HallC5×C7×C19 ⋊ C3⋊Dic3
HallC32×C5×C7 ⋊ Dic19
HallC32×C19 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C19 ⋊ C3⋊ΓL(1,𝔽16)
HallC5×C19 ⋊ C3⋊Dic21
HallC32×C7 ⋊ C19⋊AGL(1,𝔽5)
HallC32×C5 ⋊ Dic133
HallC5×C7 ⋊ C3⋊Dic57
SylowC19 ⋊ C3⋊(C3⋊(C7⋊AGL(1,𝔽5)))
SylowC32 ⋊ C7⋊(C19⋊AGL(1,𝔽5))
SylowC7 ⋊ C3⋊(C3⋊(C19⋊AGL(1,𝔽5)))
SylowC5 ⋊ C3⋊Dic399

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C5×C7×C19C4
prime radical, cosocleC32×C7×D5×C19C2
LCSG ▷ C32×C5×C7×C19
UCSC1

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5985

Polycyclic presentation:

2^2,3^2,5,7,19|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^6,g^a=g^18,e^b=e^4

Conjugacy classes & character table

2397 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 729);