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D17765 #48001052

order35530
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD17765
unambiguous semidirect productC5⋊D3553
unambiguous semidirect productC11⋊D1615
unambiguous semidirect productC17⋊D1045
unambiguous semidirect productC19⋊D935

Splittings

Fitting, socle, derived, HallC5×C11×C17×C19 ⋊ C2
HallC11×C17×C19 ⋊ D5
HallC5×C17×C19 ⋊ D11
HallC5×C11×C19 ⋊ D17
HallC5×C11×C17 ⋊ D19
HallC17×C19 ⋊ D55
HallC11×C19 ⋊ D85
HallC11×C17 ⋊ D95
HallC5×C19 ⋊ D187
HallC5×C17 ⋊ D209
HallC5×C11 ⋊ D323
SylowC19 ⋊ D935
SylowC17 ⋊ D1045
SylowC11 ⋊ D1615
SylowC5 ⋊ D3553

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C11×C17×C19C2
LCSG ▷ C5×C11×C17×C19
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 17765

A minimal faithful permutation representation — 2 generators on 52 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33)(34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52);(2,5)(3,4)(7,16)(8,15)(9,14)(10,13)(11,12)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(35,52)(36,51)(37,50)(38,49)(39,48)(40,47)(41,46)(42,45)(43,44)

Polycyclic presentation:

2,5,11,17,19|b^a=b^4,c^a=c^10,d^a=d^16,e^a=e^18

Conjugacy classes & character table

8884 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35530, 17);