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C7⋊(C9⋊(Dic11⋊C5)) #28357359

order13860
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC7⋊(C9⋊(Dic11⋊C5))
unambiguous semidirect productC9⋊(C7⋊(Dic11⋊C5))
unambiguous semidirect product(C11⋊C5)⋊Dic63
unambiguous semidirect productDic693⋊C5

Splittings

derived, HallC7×C9×C11 ⋊ C4×C5
HallC7×C9×C11⋊C5 ⋊ C4
HallDic693 ⋊ C5
HallC9×C11⋊C5 ⋊ Dic7
HallC7×C11⋊C5 ⋊ Dic9
HallC9×C11 ⋊ C5×Dic7
HallC7×C11 ⋊ C5×Dic9
HallC7×C9 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ Dic63
SylowC11 ⋊ C5×Dic63
SylowC9 ⋊ C7⋊(Dic11⋊C5)
SylowC7 ⋊ C9⋊(Dic11⋊C5)

Subgroups

subgroupG/H
center, hypercenterC2C7⋊(C9⋊AGL(1,𝔽11))
commutator, hypocenterC7×C9×C11C4×C5
FrattiniC2×C3C3⋊(C7⋊AGL(1,𝔽11))
Fitting, cosocleC2×C7×C9×C11C2×C5
socleC2×C3×C7×C11C5×D3
prime radicalC2×C3×C7×C11⋊C5D3
LCSG ▷ C7×C9×C11
UCSC1 ◁ C2

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Polycyclic presentation:

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

Conjugacy classes & character table

456 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 26);