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C23⋊((C19⋊C3)⋊AGL(1,𝔽5)) #39910738

order26220
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, derived, HallC5×C19×C23 ⋊ C3×C4
HallC19⋊(C23⋊AGL(1,𝔽5)) ⋊ C3
HallC5×C23×C19⋊C3 ⋊ C4
HallC23×C19⋊C3 ⋊ AGL(1,𝔽5)
HallC19×C23 ⋊ C3×AGL(1,𝔽5)
HallC5×C19⋊C3 ⋊ Dic23
HallC5×C23 ⋊ (C19⋊C3)⋊C4
HallC5×C19 ⋊ C3×Dic23
HallC19⋊C3 ⋊ C23⋊AGL(1,𝔽5)
SylowC23 ⋊ (C19⋊C3)⋊AGL(1,𝔽5)
SylowC19 ⋊ C3×C23⋊AGL(1,𝔽5)
SylowC5 ⋊ C23⋊((C19⋊C3)⋊C4)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C19×C23C3×C4
prime radicalD5×C23×C19⋊C3C2
cosocleD5×C19×C23C2×C3
LCSG ▷ C5×C19×C23
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2185

Polycyclic presentation:

2,3,2,5,19,23|a^2=c,d^a=d^2,e^a=e^18,f^a=f^22,e^b=e^7,d^c=d^4

Conjugacy classes & character table

423 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 28);