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C3⋊((C11⋊C5)⋊Dic41) #41028596

order27060
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊((C11⋊C5)⋊Dic41)
unambiguous semidirect product(C11⋊C5)⋊Dic123

Splittings

derived, HallC3×C11×C41 ⋊ C4×C5
HallC3×C41×C11⋊C5 ⋊ C4
HallDic1353 ⋊ C5
HallC41×C11⋊C5 ⋊ Dic3
HallC11×C41 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ Dic41
HallC3×C41 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ Dic123
SylowC41 ⋊ C3⋊(Dic11⋊C5)
HallC3×C11 ⋊ C5×Dic41
SylowC11 ⋊ C5×Dic123
SylowC3 ⋊ (C11⋊C5)⋊Dic41

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C3⋊((C11⋊C5)⋊D41)
commutator, hypocenterC3×C11×C41C4×C5
Fitting, socle, cosocleC2×C3×C11×C41C2×C5
prime radicalC2×C3×C41×C11⋊C5C2
LCSG ▷ C3×C11×C41
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5412

Polycyclic presentation:

2,3,5,11,41,2|a^2=f,b^a=b^2,d^a=d^10,e^a=e^40,d^c=d^4

Conjugacy classes & character table

876 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27060, 60);