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C7⋊(C11⋊#66776) #39910448

order26180
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC7⋊(C11⋊#66776)
unambiguous semidirect productC11⋊(C7⋊#66776)

Splittings

Fitting, socle, derived, HallC5×C7×C11×C17 ⋊ C4
HallC7×C11×C17 ⋊ AGL(1,𝔽5)
HallC5×C11×C17 ⋊ Dic7
HallC5×C7×C17 ⋊ Dic11
HallC5×C7×C11 ⋊ #595
HallC11×C17 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C17 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C17 ⋊ Dic77
HallC7×C11 ⋊ #66776
HallC5×C11 ⋊ C7⋊#595
HallC5×C7 ⋊ C11⋊#595
SylowC17 ⋊ C7⋊(C11⋊AGL(1,𝔽5))
SylowC11 ⋊ C7⋊#66776
SylowC7 ⋊ C11⋊#66776
SylowC5 ⋊ C7⋊(C11⋊#595)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C11×C17C4
prime radical, cosocleC7×C11×D85C2
LCSG ▷ C5×C7×C11×C17
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6545

Polycyclic presentation:

2^2,5,7,11,17|a^2=b,c^a=c^2,d^a=d^6,e^a=e^10,f^a=f^4,c^b=c^4,f^b=f^16

Conjugacy classes & character table

1697 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26180, 70);