D₁₇₀₀₅ #46801022

order	34010
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₇₀₀₅
unambiguous semidirect product	C₅⋊D₃₄₀₁
unambiguous semidirect product	C₁₉⋊D₈₉₅
unambiguous semidirect product	C₁₇₉⋊D₉₅

Splittings

Fitting, socle, derived, Hall	C₅×C₁₉×C₁₇₉ ⋊ C₂
Hall	C₁₉×C₁₇₉ ⋊ D₅
Hall	C₅×C₁₇₉ ⋊ D₁₉
Sylow	C₁₇₉ ⋊ D₉₅
Hall	C₅×C₁₉ ⋊ D₁₇₉
Sylow	C₁₉ ⋊ D₈₉₅
Sylow	C₅ ⋊ D₃₄₀₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₉×C₁₇₉	C₂
LCS	G ▷ C₅×C₁₉×C₁₇₉
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 203
transitive degree	μ_t(G) = 17005

A minimal faithful permutation representation — 2 generators on 203 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)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203);(2,5)(3,4)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(26,203)(27,202)(28,201)(29,200)(30,199)(31,198)(32,197)(33,196)(34,195)(35,194)(36,193)(37,192)(38,191)(39,190)(40,189)(41,188)(42,187)(43,186)(44,185)(45,184)(46,183)(47,182)(48,181)(49,180)(50,179)(51,178)(52,177)(53,176)(54,175)(55,174)(56,173)(57,172)(58,171)(59,170)(60,169)(61,168)(62,167)(63,166)(64,165)(65,164)(66,163)(67,162)(68,161)(69,160)(70,159)(71,158)(72,157)(73,156)(74,155)(75,154)(76,153)(77,152)(78,151)(79,150)(80,149)(81,148)(82,147)(83,146)(84,145)(85,144)(86,143)(87,142)(88,141)(89,140)(90,139)(91,138)(92,137)(93,136)(94,135)(95,134)(96,133)(97,132)(98,131)(99,130)(100,129)(101,128)(102,127)(103,126)(104,125)(105,124)(106,123)(107,122)(108,121)(109,120)(110,119)(111,118)(112,117)(113,116)(114,115)

Polycyclic presentation:

2,5,19,179|b^a=b^4,c^a=c^18,d^a=d^178

Conjugacy classes & character table

8504 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34010, 8);

D17005 #46801022