Finite Group Databasebeta

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C7⋊(C9⋊(D11⋊C25)) #46831383

order34650
automorphism?
homologyAbelianization (H1) = C2×C25 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC7⋊(C9⋊(D11⋊C25))
unambiguous semidirect productC9⋊(C7⋊(D11⋊C25))
unambiguous semidirect product(C11⋊C25)⋊D63
unambiguous semidirect productD693⋊C25

Splittings

derived, HallC7×C9×C11 ⋊ C2×C25
HallC7×C9×C11⋊C25 ⋊ C2
HallC9×C11⋊C25 ⋊ D7
HallC7×C11⋊C25 ⋊ D9
HallD693 ⋊ C25
HallC11⋊C25 ⋊ D63
HallC9×C11 ⋊ D7×C25
HallC7×C11 ⋊ D9×C25
HallC7×C9 ⋊ D11⋊C25
SylowC11 ⋊ C25×D63
SylowC9 ⋊ C7⋊(D11⋊C25)
SylowC7 ⋊ C9⋊(D11⋊C25)

Subgroups

subgroupG/H
center, hypercenterC5C7⋊(C9⋊AGL(1,𝔽11))
commutator, hypocenterC7×C9×C11C2×C25
FrattiniC3×C5C3⋊(C7⋊AGL(1,𝔽11))
Fitting, cosocleC5×C7×C9×C11C2×C5
socleC3×C5×C7×C11C5×D3
prime radicalC5×D693C5
LCSG ▷ C7×C9×C11
UCSC1 ◁ C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Polycyclic presentation:

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

Conjugacy classes & character table

1140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 26);