Dic₇₉₁₃ #44539583

order	31652
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic

Dic₇₉₁₃

Splittings

derived, Hall	C₄₁×C₁₉₃ ⋊ C₄
Sylow	C₁₉₃ ⋊ Dic₄₁
Sylow	C₄₁ ⋊ Dic₁₉₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇₉₁₃
commutator, hypocenter	C₄₁×C₁₉₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₄₁×C₁₉₃	C₂
LCS	G ▷ C₄₁×C₁₉₃
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 238
transitive degree	μ_t(G) = 31652

A minimal faithful permutation representation — 2 generators on 238 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)(46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238);(1,3,2,4)(6,45)(7,44)(8,43)(9,42)(10,41)(11,40)(12,39)(13,38)(14,37)(15,36)(16,35)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(47,238)(48,237)(49,236)(50,235)(51,234)(52,233)(53,232)(54,231)(55,230)(56,229)(57,228)(58,227)(59,226)(60,225)(61,224)(62,223)(63,222)(64,221)(65,220)(66,219)(67,218)(68,217)(69,216)(70,215)(71,214)(72,213)(73,212)(74,211)(75,210)(76,209)(77,208)(78,207)(79,206)(80,205)(81,204)(82,203)(83,202)(84,201)(85,200)(86,199)(87,198)(88,197)(89,196)(90,195)(91,194)(92,193)(93,192)(94,191)(95,190)(96,189)(97,188)(98,187)(99,186)(100,185)(101,184)(102,183)(103,182)(104,181)(105,180)(106,179)(107,178)(108,177)(109,176)(110,175)(111,174)(112,173)(113,172)(114,171)(115,170)(116,169)(117,168)(118,167)(119,166)(120,165)(121,164)(122,163)(123,162)(124,161)(125,160)(126,159)(127,158)(128,157)(129,156)(130,155)(131,154)(132,153)(133,152)(134,151)(135,150)(136,149)(137,148)(138,147)(139,146)(140,145)(141,144)(142,143)

Polycyclic presentation:

2,41,193,2|a^2=d,b^a=b^40,c^a=c^192

Conjugacy classes & character table

7916 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₁₅₈₂₆
maximal normal subgroup of	Dic₁₅₈₂₆

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31652, 4);

Dic7913 #44539583