D₆₉₆₃ #28358223

order	13926
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₆₉₆₃
unambiguous semidirect product	C₃⋊D₂₃₂₁
unambiguous semidirect product	C₁₁⋊D₆₃₃
unambiguous semidirect product	C₂₁₁⋊D₃₃

Splittings

Fitting, socle, derived, Hall	C₃×C₁₁×C₂₁₁ ⋊ C₂
Hall	C₁₁×C₂₁₁ ⋊ D₃
Hall	C₃×C₂₁₁ ⋊ D₁₁
Sylow	C₂₁₁ ⋊ D₃₃
Hall	C₃×C₁₁ ⋊ D₂₁₁
Sylow	C₁₁ ⋊ D₆₃₃
Sylow	C₃ ⋊ D₂₃₂₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₂₁₁	C₂
LCS	G ▷ C₃×C₁₁×C₂₁₁
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 225
transitive degree	μ_t(G) = 6963

A minimal faithful permutation representation — 2 generators on 225 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225);(2,3)(5,14)(6,13)(7,12)(8,11)(9,10)(16,225)(17,224)(18,223)(19,222)(20,221)(21,220)(22,219)(23,218)(24,217)(25,216)(26,215)(27,214)(28,213)(29,212)(30,211)(31,210)(32,209)(33,208)(34,207)(35,206)(36,205)(37,204)(38,203)(39,202)(40,201)(41,200)(42,199)(43,198)(44,197)(45,196)(46,195)(47,194)(48,193)(49,192)(50,191)(51,190)(52,189)(53,188)(54,187)(55,186)(56,185)(57,184)(58,183)(59,182)(60,181)(61,180)(62,179)(63,178)(64,177)(65,176)(66,175)(67,174)(68,173)(69,172)(70,171)(71,170)(72,169)(73,168)(74,167)(75,166)(76,165)(77,164)(78,163)(79,162)(80,161)(81,160)(82,159)(83,158)(84,157)(85,156)(86,155)(87,154)(88,153)(89,152)(90,151)(91,150)(92,149)(93,148)(94,147)(95,146)(96,145)(97,144)(98,143)(99,142)(100,141)(101,140)(102,139)(103,138)(104,137)(105,136)(106,135)(107,134)(108,133)(109,132)(110,131)(111,130)(112,129)(113,128)(114,127)(115,126)(116,125)(117,124)(118,123)(119,122)(120,121)

Polycyclic presentation:

2,3,11,211|b^a=b^2,c^a=c^10,d^a=d^210

Conjugacy classes & character table

3483 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃₃×D₂₁₁, D₁₁×D₆₃₃, D₃×D₂₃₂₁, …
maximal normal subgroup of	D₃₃×D₂₁₁, D₁₁×D₆₃₃, D₃×D₂₃₂₁, …
maximal quotient of	Dic₆₉₆₃, C₂×D₆₉₆₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13926, 9);

D6963 #28358223