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C11⋊((C49⋊C3)⋊Dic5) #44568331

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

Aliases

unambiguous semidirect productC11⋊((C49⋊C3)⋊Dic5)
unambiguous semidirect product(C49⋊C3)⋊Dic55
unambiguous semidirect productDic2695⋊C3

Splittings

derived, HallC5×C11×C49 ⋊ C3×C4
HallDic2695 ⋊ C3
HallC5×C11×C49⋊C3 ⋊ C4
HallC11×C49⋊C3 ⋊ Dic5
HallC5×C49⋊C3 ⋊ Dic11
HallC11×C49 ⋊ C3×Dic5
HallC5×C49 ⋊ C3×Dic11
HallC49⋊C3 ⋊ Dic55
HallC5×C11 ⋊ (C49⋊C3)⋊C4
SylowC49 ⋊ C3×Dic55
SylowC11 ⋊ (C49⋊C3)⋊Dic5
SylowC5 ⋊ C11⋊((C49⋊C3)⋊C4)

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(C11⋊(D49⋊C3))
commutator, hypocenterC5×C11×C49C3×C4
FrattiniC2×C7C5⋊(C11⋊AGL(1,𝔽7))
Fitting, cosocleC2×C5×C11×C49C2×C3
socleC2×C5×C7×C11AGL(1,𝔽7)
prime radicalC2×C5×C11×C49⋊C3C2
LCSG ▷ C5×C11×C49
UCSC1 ◁ C2

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10780

Polycyclic presentation:

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

Conjugacy classes & character table

1054 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 33);