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C7⋊((C11⋊C5)⋊#157) #28357573

order13860
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC7⋊((C11⋊C5)⋊#157)
unambiguous semidirect product(C11⋊C5)⋊(C7⋊#157)
unambiguous semidirect product(C7⋊(C11⋊#157))⋊C5

Splittings

Fitting, socle, derived, HallC32×C7×C11 ⋊ C4×C5
HallC32×C7×C11⋊C5 ⋊ C4
HallC7⋊(C11⋊#157) ⋊ C5
HallC32×C11⋊C5 ⋊ Dic7
HallC7×C11⋊C5 ⋊ #157
HallC32×C11 ⋊ C5×Dic7
HallC7×C11 ⋊ C5×#157
HallC32×C7 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C7⋊#157
SylowC11 ⋊ C5×C7⋊#157
SylowC32 ⋊ C7⋊(Dic11⋊C5)
SylowC7 ⋊ (C11⋊C5)⋊#157

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C7×C11C4×C5
prime radicalC7×C3⋊D3×C11⋊C5C2
cosocleC7×C11×C3⋊D3C2×C5
LCSG ▷ C32×C7×C11
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 462

Polycyclic presentation:

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

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 240);