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C3⋊(C5⋊(C7⋊D91)) #34062185

order19110
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C7

Aliases

unambiguous semidirect productC3⋊(C5⋊(C7⋊D91))
unambiguous semidirect productC5⋊(C3⋊(C7⋊D91))
unambiguous semidirect productC7⋊D1365
unambiguous semidirect productC13⋊(C3⋊(C5⋊(C7⋊D7)))

Splittings

Fitting, socle, derived, HallC3×C5×C72×C13 ⋊ C2
HallC5×C72×C13 ⋊ D3
HallC3×C72×C13 ⋊ D5
HallC3×C5×C72 ⋊ D13
HallC72×C13 ⋊ D15
HallC5×C72 ⋊ D39
HallC3×C5×C13 ⋊ C7⋊D7
HallC3×C72 ⋊ D65
HallC5×C13 ⋊ C3⋊(C7⋊D7)
SylowC72 ⋊ D195
HallC3×C13 ⋊ C5⋊(C7⋊D7)
HallC3×C5 ⋊ C7⋊D91
SylowC13 ⋊ C3⋊(C5⋊(C7⋊D7))
SylowC5 ⋊ C3⋊(C7⋊D91)
SylowC3 ⋊ C5⋊(C7⋊D91)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C72×C13C2
LCSG ▷ C3×C5×C72×C13
UCSC1

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9555

Polycyclic presentation:

2,3,5,7^2,13|b^a=b^2,c^a=c^4,d^a=d^6,e^a=e^6,f^a=f^12

Conjugacy classes & character table

4779 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD7×D1365, D91×D105, D13×C3⋊(C5⋊(C7⋊D7)), …
maximal normal subgroup ofD7×D1365, D91×D105, D13×C3⋊(C5⋊(C7⋊D7)), …
maximal quotient ofC3⋊(C7⋊Dic455), C2×C3⋊(C5⋊(C7⋊D91))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 178);