D₁₆₉₆₅ #46800231

order	33930
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₆₉₆₅
unambiguous semidirect product	C₅⋊D₃₃₉₃
unambiguous semidirect product	C₉⋊D₁₈₈₅
unambiguous semidirect product	C₁₃⋊D₁₃₀₅
unambiguous semidirect product	C₂₉⋊D₅₈₅

Splittings

Fitting, derived, Hall	C₅×C₉×C₁₃×C₂₉ ⋊ C₂
Hall	C₉×C₁₃×C₂₉ ⋊ D₅
Hall	C₅×C₁₃×C₂₉ ⋊ D₉
Hall	C₅×C₉×C₂₉ ⋊ D₁₃
Hall	C₅×C₉×C₁₃ ⋊ D₂₉
Hall	C₁₃×C₂₉ ⋊ D₄₅
Hall	C₉×C₂₉ ⋊ D₆₅
Hall	C₅×C₂₉ ⋊ D₁₁₇
Hall	C₉×C₁₃ ⋊ D₁₄₅
Hall	C₅×C₁₃ ⋊ D₂₆₁
Hall	C₅×C₉ ⋊ D₃₇₇
Sylow	C₂₉ ⋊ D₅₈₅
Sylow	C₁₃ ⋊ D₁₃₀₅
Sylow	C₉ ⋊ D₁₈₈₅
Sylow	C₅ ⋊ D₃₃₉₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₁₃×C₂₉	C₂
Frattini	C₃	D₅₆₅₅
socle	C₃×C₅×C₁₃×C₂₉	D₃
LCS	G ▷ C₅×C₉×C₁₃×C₂₉
UCS	C₁

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 56
transitive degree	μ_t(G) = 16965

A minimal faithful permutation representation — 2 generators on 56 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)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56);(2,9)(3,8)(4,7)(5,6)(11,14)(12,13)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(29,56)(30,55)(31,54)(32,53)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43)

Polycyclic presentation:

2,3,5,13,29,3|b^3=f^2,b^a=b^2f,c^a=c^4,d^a=d^12,e^a=e^28,f^a=f^2

Conjugacy classes & character table

8484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 17);

D16965 #46800231