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C3⋊((C11⋊C5)⋊#1181) #34062336

order19140
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊((C11⋊C5)⋊#1181)
unambiguous semidirect product(C11⋊C5)⋊(C3⋊#1181)
unambiguous semidirect product(C3⋊(C11⋊#1181))⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C29 ⋊ C4×C5
HallC3×C29×C11⋊C5 ⋊ C4
HallC3⋊(C11⋊#1181) ⋊ C5
HallC29×C11⋊C5 ⋊ Dic3
HallC11×C29 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ #1181
HallC3×C29 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C3⋊#1181
HallC3×C11 ⋊ C5×#1181
SylowC29 ⋊ C3⋊(Dic11⋊C5)
SylowC11 ⋊ C5×C3⋊#1181
SylowC3 ⋊ (C11⋊C5)⋊#1181

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C11×C29C4×C5
prime radicalC3×C11⋊C5×D29C2
cosocleC3×C11×D29C2×C5
LCSG ▷ C3×C11×C29
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 957

Polycyclic presentation:

2,5,2,3,11,29|a^2=c,d^a=d^2,e^a=e^10,f^a=f^17,e^b=e^4,f^c=f^28

Conjugacy classes & character table

183 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 29);