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C3⋊(C3⋊(C7⋊(Dic11⋊C5))) #28357490

order13860
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊(C3⋊(C7⋊(Dic11⋊C5)))
unambiguous semidirect productC7⋊(C3⋊(C3⋊(Dic11⋊C5)))
unambiguous semidirect product(C11⋊C5)⋊(C3⋊Dic21)
unambiguous semidirect product(C3⋊Dic231)⋊C5

Splittings

derived, HallC32×C7×C11 ⋊ C4×C5
HallC32×C7×C11⋊C5 ⋊ C4
HallC3⋊Dic231 ⋊ C5
HallC32×C11⋊C5 ⋊ Dic7
HallC7×C11⋊C5 ⋊ C3⋊Dic3
HallC32×C11 ⋊ C5×Dic7
HallC7×C11 ⋊ C5×C3⋊Dic3
HallC32×C7 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C3⋊Dic21
SylowC11 ⋊ C5×C3⋊Dic21
SylowC32 ⋊ C7⋊(Dic11⋊C5)
SylowC7 ⋊ C3⋊(C3⋊(Dic11⋊C5))

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C3⋊(C3⋊(C7⋊AGL(1,𝔽11)))
commutator, hypocenterC32×C7×C11C4×C5
Fitting, socle, cosocleC2×C32×C7×C11C2×C5
prime radicalC2×C32×C7×C11⋊C5C2
LCSG ▷ C32×C7×C11
UCSC1 ◁ C2

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Polycyclic presentation:

2,5,3^2,7,11,2|a^2=g,c^a=c^2,d^a=d^2,e^a=e^6,f^a=f^10,f^b=f^4

Conjugacy classes & character table

456 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 157);