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C3⋊(C3⋊(C5⋊AGL(1,𝔽23))) #36384759

order22770
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊(C3⋊(C5⋊AGL(1,𝔽23)))
unambiguous semidirect productC5⋊(C3⋊(C3⋊AGL(1,𝔽23)))
unambiguous semidirect product(C23⋊C11)⋊(C3⋊D15)
unambiguous semidirect product(C3⋊D345)⋊C11

Splittings

Fitting, socle, derived, HallC32×C5×C23 ⋊ C2×C11
HallC32×C5×C23⋊C11 ⋊ C2
HallC32×C23⋊C11 ⋊ D5
HallC3⋊D345 ⋊ C11
HallC5×C23⋊C11 ⋊ C3⋊D3
HallC23⋊C11 ⋊ C3⋊D15
HallC32×C23 ⋊ D5×C11
HallC5×C23 ⋊ C11×C3⋊D3
HallC32×C5 ⋊ AGL(1,𝔽23)
SylowC23 ⋊ C11×C3⋊D15
SylowC32 ⋊ C5⋊AGL(1,𝔽23)
SylowC5 ⋊ C3⋊(C3⋊AGL(1,𝔽23))

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C23C2×C11
LCSG ▷ C32×C5×C23
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1035

Polycyclic presentation:

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

Conjugacy classes & character table

309 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22770, 43);