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C3⋊(C5⋊D1105) #45684198

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

Aliases

unambiguous semidirect productC3⋊(C5⋊D1105)
unambiguous semidirect productC5⋊D3315
unambiguous semidirect productC13⋊(C3⋊(C5⋊D85))
unambiguous semidirect productC17⋊(C3⋊(C5⋊D65))

Splittings

Fitting, socle, derived, HallC3×C52×C13×C17 ⋊ C2
HallC52×C13×C17 ⋊ D3
HallC3×C52×C17 ⋊ D13
HallC3×C52×C13 ⋊ D17
HallC3×C13×C17 ⋊ C5⋊D5
HallC52×C17 ⋊ D39
HallC52×C13 ⋊ D51
HallC13×C17 ⋊ C3⋊(C5⋊D5)
HallC3×C52 ⋊ D221
HallC3×C17 ⋊ C5⋊D65
HallC3×C13 ⋊ C5⋊D85
SylowC52 ⋊ D663
SylowC17 ⋊ C3⋊(C5⋊D65)
SylowC13 ⋊ C3⋊(C5⋊D85)
SylowC3 ⋊ C5⋊D1105

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C13×C17C2
LCSG ▷ C3×C52×C13×C17
UCSC1

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16575

Polycyclic presentation:

2,3,5^2,13,17|b^a=b^2,c^a=c^4,d^a=d^4,e^a=e^12,f^a=f^16

Conjugacy classes & character table

8289 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 80);