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C3⋊((C23⋊C11)⋊AGL(1,𝔽5)) #29503252

order15180
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊((C23⋊C11)⋊AGL(1,𝔽5))
unambiguous semidirect product(C23⋊C11)⋊ΓL(1,𝔽16)
unambiguous semidirect product(C3⋊(C23⋊AGL(1,𝔽5)))⋊C11

Splittings

Fitting, socle, derived, HallC3×C5×C23 ⋊ C4×C11
HallC3×C5×C23⋊C11 ⋊ C4
HallC3⋊(C23⋊AGL(1,𝔽5)) ⋊ C11
HallC5×C23⋊C11 ⋊ Dic3
HallC3×C23⋊C11 ⋊ AGL(1,𝔽5)
HallC23⋊C11 ⋊ ΓL(1,𝔽16)
HallC5×C23 ⋊ C11×Dic3
HallC3×C23 ⋊ C11×AGL(1,𝔽5)
SylowC23 ⋊ C11×ΓL(1,𝔽16)
HallC3×C5 ⋊ Dic23⋊C11
SylowC5 ⋊ C3⋊(Dic23⋊C11)
SylowC3 ⋊ (C23⋊C11)⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C23C4×C11
prime radicalC3×D5×C23⋊C11C2
cosocleC3×D5×C23C2×C11
LCSG ▷ C3×C5×C23
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 345

Polycyclic presentation:

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

Conjugacy classes & character table

111 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 38);