C₃×D₅₁₈₃ #44527326

order	31098
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₅₁₈₃
unambiguous semidirect product	C₇₁⋊(C₃×D₇₃)

Splittings

Fitting, socle, Hall	C₃×C₇₁×C₇₃ ⋊ C₂
derived, Hall	C₇₁×C₇₃ ⋊ C₂×C₃
Hall	C₃×C₇₃ ⋊ D₇₁
Hall	C₃×C₇₁ ⋊ D₇₃
Sylow	C₇₃ ⋊ C₃×D₇₁
Sylow	C₇₁ ⋊ C₃×D₇₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₅₁₈₃
commutator, cosocle, hypocenter	C₇₁×C₇₃	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇₁×C₇₃	C₂
LCS	G ▷ C₇₁×C₇₃
UCS	C₁ ◁ C₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 147
transitive degree	μ_t(G) = 15549

A minimal faithful permutation representation — 2 generators on 147 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);(5,74)(6,73)(7,72)(8,71)(9,70)(10,69)(11,68)(12,67)(13,66)(14,65)(15,64)(16,63)(17,62)(18,61)(19,60)(20,59)(21,58)(22,57)(23,56)(24,55)(25,54)(26,53)(27,52)(28,51)(29,50)(30,49)(31,48)(32,47)(33,46)(34,45)(35,44)(36,43)(37,42)(38,41)(39,40)(76,147)(77,146)(78,145)(79,144)(80,143)(81,142)(82,141)(83,140)(84,139)(85,138)(86,137)(87,136)(88,135)(89,134)(90,133)(91,132)(92,131)(93,130)(94,129)(95,128)(96,127)(97,126)(98,125)(99,124)(100,123)(101,122)(102,121)(103,120)(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)

Conjugacy classes & character table

7779 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31098, 5);

C3×D5183 #44527326