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C11⋊((C49⋊C3)⋊AGL(1,𝔽5)) #44568352

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

Aliases

unambiguous semidirect productC11⋊((C49⋊C3)⋊AGL(1,𝔽5))
unambiguous semidirect product(C49⋊C3)⋊(C11⋊AGL(1,𝔽5))
unambiguous semidirect product(C11⋊(C49⋊AGL(1,𝔽5)))⋊C3

Splittings

Fitting, derived, HallC5×C11×C49 ⋊ C3×C4
HallC11⋊(C49⋊AGL(1,𝔽5)) ⋊ C3
HallC5×C11×C49⋊C3 ⋊ C4
HallC11×C49⋊C3 ⋊ AGL(1,𝔽5)
HallC5×C49⋊C3 ⋊ Dic11
HallC11×C49 ⋊ C3×AGL(1,𝔽5)
HallC5×C49 ⋊ C3×Dic11
HallC49⋊C3 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C11 ⋊ (C49⋊C3)⋊C4
SylowC49 ⋊ C3×C11⋊AGL(1,𝔽5)
SylowC11 ⋊ (C49⋊C3)⋊AGL(1,𝔽5)
SylowC5 ⋊ C11⋊((C49⋊C3)⋊C4)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, hypocenterC5×C11×C49C3×C4
FrattiniC7C11⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))
socleC5×C7×C11ΓL(1,𝔽8)⋊C4
prime radicalD5×C11×C49⋊C3C2
cosocleD5×C11×C49C2×C3
LCSG ▷ C5×C11×C49
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2695

Polycyclic presentation:

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

Conjugacy classes & character table

427 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 54);