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C3⋊(C11⋊(C49⋊AGL(1,𝔽5))) #44568396

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

Aliases

unambiguous semidirect productC3⋊(C11⋊(C49⋊AGL(1,𝔽5)))
unambiguous semidirect productC11⋊(C3⋊(C49⋊AGL(1,𝔽5)))
unambiguous semidirect productC49⋊(C3⋊(C11⋊AGL(1,𝔽5)))

Splittings

Fitting, derived, HallC3×C5×C11×C49 ⋊ C4
HallC5×C11×C49 ⋊ Dic3
HallC3×C11×C49 ⋊ AGL(1,𝔽5)
HallC3×C5×C49 ⋊ Dic11
HallC11×C49 ⋊ ΓL(1,𝔽16)
HallC5×C49 ⋊ Dic33
HallC3×C5×C11 ⋊ Dic49
HallC3×C49 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C11 ⋊ Dic147
SylowC49 ⋊ C3⋊(C11⋊AGL(1,𝔽5))
HallC3×C11 ⋊ C49⋊AGL(1,𝔽5)
HallC3×C5 ⋊ Dic539
SylowC11 ⋊ C3⋊(C49⋊AGL(1,𝔽5))
SylowC5 ⋊ Dic1617
SylowC3 ⋊ C11⋊(C49⋊AGL(1,𝔽5))

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, hypocenterC3×C5×C11×C49C4
FrattiniC7C3⋊(C7⋊(C11⋊AGL(1,𝔽5)))
socleC3×C5×C7×C11Dic7
prime radicalC3×C7×D5×C11D7
cosocleC3×D5×C11×C49C2
LCSG ▷ C3×C5×C11×C49
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Polycyclic presentation:

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

Conjugacy classes & character table

3237 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 98);