D₁₇₃₀₁ #46829490

order	34602
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₇₃₀₁
unambiguous semidirect product	C₃⋊D₅₇₆₇
unambiguous semidirect product	C₇₃⋊D₂₃₇
unambiguous semidirect product	C₇₉⋊D₂₁₉

Splittings

Fitting, socle, derived, Hall	C₃×C₇₃×C₇₉ ⋊ C₂
Hall	C₇₃×C₇₉ ⋊ D₃
Hall	C₃×C₇₉ ⋊ D₇₃
Hall	C₃×C₇₃ ⋊ D₇₉
Sylow	C₇₉ ⋊ D₂₁₉
Sylow	C₇₃ ⋊ D₂₃₇
Sylow	C₃ ⋊ D₅₇₆₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇₃×C₇₉	C₂
LCS	G ▷ C₃×C₇₃×C₇₉
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 155
transitive degree	μ_t(G) = 17301

A minimal faithful permutation representation — 2 generators on 155 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)(77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155);(2,3)(5,76)(6,75)(7,74)(8,73)(9,72)(10,71)(11,70)(12,69)(13,68)(14,67)(15,66)(16,65)(17,64)(18,63)(19,62)(20,61)(21,60)(22,59)(23,58)(24,57)(25,56)(26,55)(27,54)(28,53)(29,52)(30,51)(31,50)(32,49)(33,48)(34,47)(35,46)(36,45)(37,44)(38,43)(39,42)(40,41)(78,155)(79,154)(80,153)(81,152)(82,151)(83,150)(84,149)(85,148)(86,147)(87,146)(88,145)(89,144)(90,143)(91,142)(92,141)(93,140)(94,139)(95,138)(96,137)(97,136)(98,135)(99,134)(100,133)(101,132)(102,131)(103,130)(104,129)(105,128)(106,127)(107,126)(108,125)(109,124)(110,123)(111,122)(112,121)(113,120)(114,119)(115,118)(116,117)

Polycyclic presentation:

2,3,73,79|b^a=b^2,c^a=c^72,d^a=d^78

Conjugacy classes & character table

8652 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34602, 12);

D17301 #46829490