Dic₉₄₅₇ #49180752

order	37828
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₉₄₅₇
unambiguous semidirect product	C₄₉⋊Dic₁₉₃

Splittings

derived, Hall	C₄₉×C₁₉₃ ⋊ C₄
Sylow	C₁₉₃ ⋊ Dic₄₉
Sylow	C₄₉ ⋊ Dic₁₉₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₉₄₅₇
commutator, hypocenter	C₄₉×C₁₉₃	C₄
Frattini	C₂×C₇	D₁₃₅₁
Fitting, cosocle	C₂×C₄₉×C₁₉₃	C₂
socle, prime radical	C₂×C₇×C₁₉₃	D₇
LCS	G ▷ C₄₉×C₁₉₃
UCS	C₁ ◁ C₂

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 246
transitive degree	μ_t(G) = 37828

A minimal faithful permutation representation — 2 generators on 246 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)(54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246);(1,3,2,4)(6,53)(7,52)(8,51)(9,50)(10,49)(11,48)(12,47)(13,46)(14,45)(15,44)(16,43)(17,42)(18,41)(19,40)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)(55,246)(56,245)(57,244)(58,243)(59,242)(60,241)(61,240)(62,239)(63,238)(64,237)(65,236)(66,235)(67,234)(68,233)(69,232)(70,231)(71,230)(72,229)(73,228)(74,227)(75,226)(76,225)(77,224)(78,223)(79,222)(80,221)(81,220)(82,219)(83,218)(84,217)(85,216)(86,215)(87,214)(88,213)(89,212)(90,211)(91,210)(92,209)(93,208)(94,207)(95,206)(96,205)(97,204)(98,203)(99,202)(100,201)(101,200)(102,199)(103,198)(104,197)(105,196)(106,195)(107,194)(108,193)(109,192)(110,191)(111,190)(112,189)(113,188)(114,187)(115,186)(116,185)(117,184)(118,183)(119,182)(120,181)(121,180)(122,179)(123,178)(124,177)(125,176)(126,175)(127,174)(128,173)(129,172)(130,171)(131,170)(132,169)(133,168)(134,167)(135,166)(136,165)(137,164)(138,163)(139,162)(140,161)(141,160)(142,159)(143,158)(144,157)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151)

Polycyclic presentation:

2,7,193,2,7|a^2=d,b^7=e^6,b^a=b^6e,c^a=c^192,e^a=e^6

Conjugacy classes & character table

9460 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37828, 4);

Dic9457 #49180752