D₁₅₄₈₁ #44526320

order	30962
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₅₄₈₁
unambiguous semidirect product	C₁₁₃⋊D₁₃₇
unambiguous semidirect product	C₁₃₇⋊D₁₁₃

Splittings

Fitting, socle, derived, Hall	C₁₁₃×C₁₃₇ ⋊ C₂
Sylow	C₁₃₇ ⋊ D₁₁₃
Sylow	C₁₁₃ ⋊ D₁₃₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁₃×C₁₃₇	C₂
LCS	G ▷ C₁₁₃×C₁₃₇
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 250
transitive degree	μ_t(G) = 15481

A minimal faithful permutation representation — 2 generators on 250 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)(114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250);(2,113)(3,112)(4,111)(5,110)(6,109)(7,108)(8,107)(9,106)(10,105)(11,104)(12,103)(13,102)(14,101)(15,100)(16,99)(17,98)(18,97)(19,96)(20,95)(21,94)(22,93)(23,92)(24,91)(25,90)(26,89)(27,88)(28,87)(29,86)(30,85)(31,84)(32,83)(33,82)(34,81)(35,80)(36,79)(37,78)(38,77)(39,76)(40,75)(41,74)(42,73)(43,72)(44,71)(45,70)(46,69)(47,68)(48,67)(49,66)(50,65)(51,64)(52,63)(53,62)(54,61)(55,60)(56,59)(57,58)(115,250)(116,249)(117,248)(118,247)(119,246)(120,245)(121,244)(122,243)(123,242)(124,241)(125,240)(126,239)(127,238)(128,237)(129,236)(130,235)(131,234)(132,233)(133,232)(134,231)(135,230)(136,229)(137,228)(138,227)(139,226)(140,225)(141,224)(142,223)(143,222)(144,221)(145,220)(146,219)(147,218)(148,217)(149,216)(150,215)(151,214)(152,213)(153,212)(154,211)(155,210)(156,209)(157,208)(158,207)(159,206)(160,205)(161,204)(162,203)(163,202)(164,201)(165,200)(166,199)(167,198)(168,197)(169,196)(170,195)(171,194)(172,193)(173,192)(174,191)(175,190)(176,189)(177,188)(178,187)(179,186)(180,185)(181,184)(182,183)

Polycyclic presentation:

2,113,137|b^a=b^112,c^a=c^136

Conjugacy classes & character table

7742 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₅₄₈₁
maximal normal subgroup of	C₂×D₁₅₄₈₁
maximal quotient of	Dic₁₅₄₈₁, C₂×D₁₅₄₈₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30962, 3);

D15481 #44526320