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(C11⋊C5)⋊((C49⋊C3)⋊C4) #44568334

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C11⋊C5)⋊((C49⋊C3)⋊C4)
unambiguous semidirect product(C49⋊C3)⋊(Dic11⋊C5)
unambiguous semidirect product(C11⋊((C49⋊C3)⋊C4))⋊C5
unambiguous semidirect product(C49⋊(Dic11⋊C5))⋊C3

Splittings

derived, HallC11×C49 ⋊ C3×C4×C5
HallC49⋊(Dic11⋊C5) ⋊ C3
HallC11⋊C5×C49⋊C3 ⋊ C4
HallC11⋊((C49⋊C3)⋊C4) ⋊ C5
HallC49×C11⋊C5 ⋊ C3×C4
HallDic539 ⋊ C3×C5
HallC11×C49⋊C3 ⋊ C4×C5
HallC49⋊C3 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ (C49⋊C3)⋊C4
SylowC49 ⋊ C3×Dic11⋊C5
SylowC11 ⋊ C5×(C49⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2(C11⋊C5)⋊(D49⋊C3)
commutator, hypocenterC11×C49C3×C4×C5
FrattiniC2×C7ΓL(1,𝔽8)⋊AGL(1,𝔽11)
Fitting, cosocleC2×C11×C49C2×C3×C5
socleC2×C7×C11C5×AGL(1,𝔽7)
prime radicalC2×C11⋊C5×C49⋊C3C2
LCSG ▷ C11×C49
UCSC1 ◁ C2

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2156

Polycyclic presentation:

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

Conjugacy classes & character table

178 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 36);