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C3⋊(C49⋊(Dic11⋊C5)) #44568324

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

Aliases

unambiguous semidirect productC3⋊(C49⋊(Dic11⋊C5))
unambiguous semidirect productC49⋊(C3⋊(Dic11⋊C5))
unambiguous semidirect product(C11⋊C5)⋊Dic147
unambiguous semidirect productDic1617⋊C5

Splittings

derived, HallC3×C11×C49 ⋊ C4×C5
HallC3×C49×C11⋊C5 ⋊ C4
HallDic1617 ⋊ C5
HallC49×C11⋊C5 ⋊ Dic3
HallC11×C49 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ Dic49
HallC3×C49 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ Dic147
SylowC49 ⋊ C3⋊(Dic11⋊C5)
HallC3×C11 ⋊ C5×Dic49
SylowC11 ⋊ C5×Dic147
SylowC3 ⋊ C49⋊(Dic11⋊C5)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C49⋊AGL(1,𝔽11))
commutator, hypocenterC3×C11×C49C4×C5
FrattiniC2×C7C3⋊(C7⋊AGL(1,𝔽11))
Fitting, cosocleC2×C3×C11×C49C2×C5
socleC2×C3×C7×C11C5×D7
prime radicalC2×C3×C7×C11⋊C5D7
LCSG ▷ C3×C11×C49
UCSC1 ◁ C2

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6468

Polycyclic presentation:

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

Conjugacy classes & character table

1044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 26);