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C3⋊(C3⋊(C5⋊D385)) #46831685

order34650
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C3×C5

Aliases

unambiguous semidirect productC3⋊(C3⋊(C5⋊D385))
unambiguous semidirect productC5⋊(C3⋊D1155)
unambiguous semidirect productC7⋊(C3⋊(C3⋊(C5⋊D55)))
unambiguous semidirect productC11⋊(C3⋊(C3⋊(C5⋊D35)))

Splittings

Fitting, socle, derived, HallC32×C52×C7×C11 ⋊ C2
HallC32×C52×C11 ⋊ D7
HallC52×C7×C11 ⋊ C3⋊D3
HallC32×C52×C7 ⋊ D11
HallC32×C7×C11 ⋊ C5⋊D5
HallC52×C11 ⋊ C3⋊D21
HallC32×C52 ⋊ D77
HallC52×C7 ⋊ C3⋊D33
HallC32×C11 ⋊ C5⋊D35
HallC7×C11 ⋊ C3⋊(C3⋊(C5⋊D5))
HallC32×C7 ⋊ C5⋊D55
SylowC52 ⋊ C3⋊D231
SylowC11 ⋊ C3⋊(C3⋊(C5⋊D35))
SylowC32 ⋊ C5⋊D385
SylowC7 ⋊ C3⋊(C3⋊(C5⋊D55))

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C7×C11C2
LCSG ▷ C32×C52×C7×C11
UCSC1

384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Polycyclic presentation:

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

Conjugacy classes & character table

8664 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 328);