C₃×D₅₈₉₃ #47977860

order	35358
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₅₈₉₃
unambiguous semidirect product	C₇₁⋊(C₃×D₈₃)
unambiguous semidirect product	C₈₃⋊(C₃×D₇₁)

Splittings

Fitting, socle, Hall	C₃×C₇₁×C₈₃ ⋊ C₂
derived, Hall	C₇₁×C₈₃ ⋊ C₂×C₃
Hall	C₃×C₈₃ ⋊ D₇₁
Hall	C₃×C₇₁ ⋊ D₈₃
Sylow	C₈₃ ⋊ C₃×D₇₁
Sylow	C₇₁ ⋊ C₃×D₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₅₈₉₃
commutator, cosocle, hypocenter	C₇₁×C₈₃	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇₁×C₈₃	C₂
LCS	G ▷ C₇₁×C₈₃
UCS	C₁ ◁ C₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 157
transitive degree	μ_t(G) = 17679

A minimal faithful permutation representation — 2 generators on 157 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);(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)(76,157)(77,156)(78,155)(79,154)(80,153)(81,152)(82,151)(83,150)(84,149)(85,148)(86,147)(87,146)(88,145)(89,144)(90,143)(91,142)(92,141)(93,140)(94,139)(95,138)(96,137)(97,136)(98,135)(99,134)(100,133)(101,132)(102,131)(103,130)(104,129)(105,128)(106,127)(107,126)(108,125)(109,124)(110,123)(111,122)(112,121)(113,120)(114,119)(115,118)(116,117)

Conjugacy classes & character table

8844 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35358, 4);

C3×D5893 #47977860