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C3⋊(C19⋊(C23⋊AGL(1,𝔽5))) #39910774

order26220
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C19⋊(C23⋊AGL(1,𝔽5)))
unambiguous semidirect productC19⋊(C3⋊(C23⋊AGL(1,𝔽5)))
unambiguous semidirect productC23⋊(C3⋊(C19⋊AGL(1,𝔽5)))

Splittings

Fitting, socle, derived, HallC3×C5×C19×C23 ⋊ C4
HallC5×C19×C23 ⋊ Dic3
HallC3×C19×C23 ⋊ AGL(1,𝔽5)
HallC19×C23 ⋊ ΓL(1,𝔽16)
HallC3×C5×C23 ⋊ Dic19
HallC3×C5×C19 ⋊ Dic23
HallC5×C23 ⋊ Dic57
HallC5×C19 ⋊ Dic69
HallC3×C23 ⋊ C19⋊AGL(1,𝔽5)
HallC3×C19 ⋊ C23⋊AGL(1,𝔽5)
SylowC23 ⋊ C3⋊(C19⋊AGL(1,𝔽5))
SylowC19 ⋊ C3⋊(C23⋊AGL(1,𝔽5))
HallC3×C5 ⋊ Dic437
SylowC5 ⋊ Dic1311
SylowC3 ⋊ C19⋊(C23⋊AGL(1,𝔽5))

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C19×C23C4
prime radical, cosocleC3×D5×C19×C23C2
LCSG ▷ C3×C5×C19×C23
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6555

Polycyclic presentation:

2^2,3,5,19,23|a^2=b,c^a=c^2,d^a=d^2,e^a=e^18,f^a=f^22,d^b=d^4

Conjugacy classes & character table

2625 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 64);