Finite Group Databasebeta

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C3⋊(C3⋊(C11⋊#63122)) #38788271

order25740
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊(C3⋊(C11⋊#63122))
unambiguous semidirect productC11⋊(C3⋊(C3⋊#63122))

Splittings

Fitting, socle, derived, HallC32×C5×C11×C13 ⋊ C4
HallC32×C11×C13 ⋊ AGL(1,𝔽5)
HallC5×C11×C13 ⋊ C3⋊Dic3
HallC32×C5×C13 ⋊ Dic11
HallC32×C5×C11 ⋊ #261
HallC11×C13 ⋊ C3⋊ΓL(1,𝔽16)
HallC32×C13 ⋊ C11⋊AGL(1,𝔽5)
HallC32×C11 ⋊ #63122
HallC5×C13 ⋊ C3⋊Dic33
HallC5×C11 ⋊ C3⋊(C3⋊#261)
HallC32×C5 ⋊ C11⋊#261
SylowC13 ⋊ C3⋊(C3⋊(C11⋊AGL(1,𝔽5)))
SylowC11 ⋊ C3⋊(C3⋊#63122)
SylowC32 ⋊ C11⋊#63122
SylowC5 ⋊ C3⋊(C3⋊(C11⋊#261))

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C5×C11×C13C4
prime radical, cosocleC32×C11×D65C2
LCSG ▷ C32×C5×C11×C13
UCSC1

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6435

Polycyclic presentation:

2^2,3^2,5,11,13|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^10,g^a=g^5,e^b=e^4,g^b=g^12

Conjugacy classes & character table

1686 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 502);