D₉₇₃₅ #34085696

order	19470
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₉₇₃₅
unambiguous semidirect product	C₃⋊D₃₂₄₅
unambiguous semidirect product	C₅⋊D₁₉₄₇
unambiguous semidirect product	C₁₁⋊D₈₈₅
unambiguous semidirect product	C₅₉⋊D₁₆₅

Splittings

Fitting, socle, derived, Hall	C₃×C₅×C₁₁×C₅₉ ⋊ C₂
Hall	C₅×C₁₁×C₅₉ ⋊ D₃
Hall	C₃×C₁₁×C₅₉ ⋊ D₅
Hall	C₃×C₅×C₅₉ ⋊ D₁₁
Hall	C₁₁×C₅₉ ⋊ D₁₅
Hall	C₅×C₅₉ ⋊ D₃₃
Hall	C₃×C₅₉ ⋊ D₅₅
Hall	C₃×C₅×C₁₁ ⋊ D₅₉
Sylow	C₅₉ ⋊ D₁₆₅
Hall	C₅×C₁₁ ⋊ D₁₇₇
Hall	C₃×C₁₁ ⋊ D₂₉₅
Hall	C₃×C₅ ⋊ D₆₄₉
Sylow	C₁₁ ⋊ D₈₈₅
Sylow	C₅ ⋊ D₁₉₄₇
Sylow	C₃ ⋊ D₃₂₄₅

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₁×C₅₉	C₂
LCS	G ▷ C₃×C₅×C₁₁×C₅₉
UCS	C₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 78
transitive degree	μ_t(G) = 9735

A minimal faithful permutation representation — 2 generators on 78 points:

(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78);(2,3)(5,8)(6,7)(10,19)(11,18)(12,17)(13,16)(14,15)(21,78)(22,77)(23,76)(24,75)(25,74)(26,73)(27,72)(28,71)(29,70)(30,69)(31,68)(32,67)(33,66)(34,65)(35,64)(36,63)(37,62)(38,61)(39,60)(40,59)(41,58)(42,57)(43,56)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)

Polycyclic presentation:

2,3,5,11,59|b^a=b^2,c^a=c^4,d^a=d^10,e^a=e^58

Conjugacy classes & character table

4869 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₉₂₀₅
maximal quotient of	D₂₉₂₀₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19470, 17);

D9735 #34085696