#30633200

order	16131
automorphism	?
homology	Abelianization (H₁) = C₃ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₁₉×C₂₈₃ ⋊ C₃
Sylow	C₂₈₃ ⋊ C₁₉⋊C₃
Sylow	C₁₉ ⋊ C₂₈₃⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₉×C₂₈₃	C₃
LCS	G ▷ C₁₉×C₂₈₃
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 302
transitive degree	μ_t(G) = 5377

A minimal faithful permutation representation — 2 generators on 302 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,92)(57,75,89)(60,78,86)(63,81,83)(66,84,80)(69,87,77)(71,90,74)(73,94,117)(76,97,114)(79,100,111)(82,103,108)(85,106,105)(88,109,102)(91,112,99)(93,115,96)(95,119,145)(98,122,142)(101,125,139)(104,128,136)(107,131,133)(110,134,130)(113,137,127)(116,140,124)(118,143,121)(120,147,175)(123,150,172)(126,153,170)(129,156,167)(132,159,164)(135,162,161)(138,165,158)(141,168,155)(144,148,152)(146,173,149)(151,178,202)(154,181,200)(157,184,198)(160,187,195)(163,190,192)(166,193,189)(169,196,186)(171,179,183)(174,201,180)(176,203,177)(182,206,225)(185,208,224)(188,211,222)(191,214,219)(194,217,216)(197,220,213)(199,207,210)(204,226,205)(209,227,243)(212,229,242)(215,232,240)(218,235,237)(221,238,234)(223,228,231)(230,244,257)(233,246,256)(236,249,254)(239,252,251)(241,245,248)(247,258,268)(250,260,267)(253,263,265)(255,259,262)(261,269,276)(264,271,275)(266,270,273)(272,277,281)(274,278,280)(279,282,283)(285,286,288)(287,290,291)(289,293,292)(294,298,296)(295,299,297)(300,302,301);(1,2,4,8,15,25,38,54,73,95,120,148,115,70,89,111,136,164,192,216,234,248,227,181,122,72,93,116,141,169,197,221,239,253,264,272,278,263,235,190,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,179,140,90,51,67,86,108,133,161,189,213,231,206,150,94,118,144,171,199,223,241,255,266,274,279,282,271,249,214,159,103,59,27,7,13,21,31,44,60,79,101,126,154,182,207,168,112,68,35,48,64,83,105,130,158,186,210,178,119,146,174,175,202,225,243,257,268,276,281,283,277,260,232,187,128,78,40,14,23,34,47,63,82,104,129,157,185,209,228,196,137,87,49,22,32,45,61,80,102,127,155,183,147,176,204,203,145,172,200,224,242,256,267,275,280,269,246,211,156,100,56,24,36,50,66,85,107,132,160,188,212,230,245,220,165,109,65,33,12,19,29,42,58,77,99,124,152,180,205,226,173,117,142,170,198,222,240,254,265,273,258,229,184,125,75,37,52,69,88,110,135,163,191,215,233,247,259,238,193,134,84,46,20,5,9,16,26,39,55,74,96,121,149,177,201,143,92,114,139,167,195,219,237,251,262,244,208,153,97,53,71,91,113,138,166,194,218,236,250,261,270,252,217,162,106,62,30,10)(284,285,287,291,296,301,298,286,289,294,299,288,292,297,290,295,300,302,293)

Polycyclic presentation:

3,19,283|b^a=b^7,c^a=c^44

Conjugacy classes & character table

1795 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×#30633200, #44567538, #44567542, …
maximal normal subgroup of	C₂×#30633200, #44567538, #44567542, …
maximal quotient of	C₂×#30633200

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16131, 3);