D₁₂₅₃₃ #38736844

order	25066
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₂₅₃₃
unambiguous semidirect product	C₈₃⋊D₁₅₁
unambiguous semidirect product	C₁₅₁⋊D₈₃

Splittings

Fitting, socle, derived, Hall	C₈₃×C₁₅₁ ⋊ C₂
Sylow	C₁₅₁ ⋊ D₈₃
Sylow	C₈₃ ⋊ D₁₅₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₈₃×C₁₅₁	C₂
LCS	G ▷ C₈₃×C₁₅₁
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 234
transitive degree	μ_t(G) = 12533

A minimal faithful permutation representation — 2 generators on 234 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);(2,83)(3,82)(4,81)(5,80)(6,79)(7,78)(8,77)(9,76)(10,75)(11,74)(12,73)(13,72)(14,71)(15,70)(16,69)(17,68)(18,67)(19,66)(20,65)(21,64)(22,63)(23,62)(24,61)(25,60)(26,59)(27,58)(28,57)(29,56)(30,55)(31,54)(32,53)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43)(85,234)(86,233)(87,232)(88,231)(89,230)(90,229)(91,228)(92,227)(93,226)(94,225)(95,224)(96,223)(97,222)(98,221)(99,220)(100,219)(101,218)(102,217)(103,216)(104,215)(105,214)(106,213)(107,212)(108,211)(109,210)(110,209)(111,208)(112,207)(113,206)(114,205)(115,204)(116,203)(117,202)(118,201)(119,200)(120,199)(121,198)(122,197)(123,196)(124,195)(125,194)(126,193)(127,192)(128,191)(129,190)(130,189)(131,188)(132,187)(133,186)(134,185)(135,184)(136,183)(137,182)(138,181)(139,180)(140,179)(141,178)(142,177)(143,176)(144,175)(145,174)(146,173)(147,172)(148,171)(149,170)(150,169)(151,168)(152,167)(153,166)(154,165)(155,164)(156,163)(157,162)(158,161)(159,160)

Polycyclic presentation:

2,83,151|b^a=b^82,c^a=c^150

Conjugacy classes & character table

6268 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₂₅₃₃
maximal normal subgroup of	C₂×D₁₂₅₃₃
maximal quotient of	Dic₁₂₅₃₃, C₂×D₁₂₅₃₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25066, 3);

D12533 #38736844