Finite Group Databasebeta

← Prev (#29503303) Next (#29503305) →

C3⋊(C11⋊(C23⋊AGL(1,𝔽5))) #29503304

order15180
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C11⋊(C23⋊AGL(1,𝔽5)))
unambiguous semidirect productC11⋊(C3⋊(C23⋊AGL(1,𝔽5)))
unambiguous semidirect productC23⋊(C3⋊(C11⋊AGL(1,𝔽5)))

Splittings

Fitting, socle, derived, HallC3×C5×C11×C23 ⋊ C4
HallC5×C11×C23 ⋊ Dic3
HallC3×C11×C23 ⋊ AGL(1,𝔽5)
HallC3×C5×C23 ⋊ Dic11
HallC11×C23 ⋊ ΓL(1,𝔽16)
HallC3×C5×C11 ⋊ Dic23
HallC5×C23 ⋊ Dic33
HallC3×C23 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C11 ⋊ Dic69
HallC3×C11 ⋊ C23⋊AGL(1,𝔽5)
SylowC23 ⋊ C3⋊(C11⋊AGL(1,𝔽5))
HallC3×C5 ⋊ Dic253
SylowC11 ⋊ C3⋊(C23⋊AGL(1,𝔽5))
SylowC5 ⋊ Dic759
SylowC3 ⋊ C11⋊(C23⋊AGL(1,𝔽5))

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C11×C23C4
prime radical, cosocleC3×D5×C11×C23C2
LCSG ▷ C3×C5×C11×C23
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3795

Polycyclic presentation:

2^2,3,5,11,23|a^2=b,c^a=c^2,d^a=d^2,e^a=e^10,f^a=f^22,d^b=d^4

Conjugacy classes & character table

1521 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 90);