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C17⋊((C5⋊D5)⋊(C13⋊C3)) #45684159

order33150
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C5

Aliases

unambiguous semidirect productC17⋊((C5⋊D5)⋊(C13⋊C3))
unambiguous semidirect product(C5⋊D85)⋊(C13⋊C3)

Splittings

Fitting, socle, derived, HallC52×C13×C17 ⋊ C2×C3
HallC17×C13⋊(C52⋊C3) ⋊ C2
HallC13×C5⋊D85 ⋊ C3
HallC13⋊(C52⋊C3) ⋊ D17
HallC5⋊D85 ⋊ C13⋊C3
HallC52×C17 ⋊ C2×C13⋊C3
HallC52×C13 ⋊ C3×D17
HallC13×C17 ⋊ (C5⋊D5)⋊C3
SylowC52 ⋊ D17×C13⋊C3
SylowC17 ⋊ (C5⋊D5)⋊(C13⋊C3)
SylowC13 ⋊ C17⋊((C5⋊D5)⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C13×C17C2×C3
LCSG ▷ C52×C13×C17
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3315

Polycyclic presentation:

2,3,5^2,13,17|c^a=c^4,d^a=d^4,f^a=f^16,c^b=cd,d^b=c^2d^3,e^b=e^3

Conjugacy classes & character table

954 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 41);