C₃×D₄₉₄₉ #44445940

order	29694
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₄₉₄₉
unambiguous semidirect product	C₁₀₁⋊(C₃×D₄₉)

Splittings

Fitting, Hall	C₃×C₄₉×C₁₀₁ ⋊ C₂
derived, Hall	C₄₉×C₁₀₁ ⋊ C₂×C₃
Hall	C₃×C₁₀₁ ⋊ D₄₉
Hall	C₃×C₄₉ ⋊ D₁₀₁
Sylow	C₁₀₁ ⋊ C₃×D₄₉
Sylow	C₄₉ ⋊ C₃×D₁₀₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₄₉₄₉
commutator, cosocle, hypocenter	C₄₉×C₁₀₁	C₂×C₃
Frattini	C₇	C₃×D₇₀₇
Fitting	C₃×C₄₉×C₁₀₁	C₂
socle	C₃×C₇×C₁₀₁	D₇
LCS	G ▷ C₄₉×C₁₀₁
UCS	C₁ ◁ C₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 153
transitive degree	μ_t(G) = 14847

A minimal faithful permutation representation — 2 generators on 153 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);(5,52)(6,51)(7,50)(8,49)(9,48)(10,47)(11,46)(12,45)(13,44)(14,43)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)(54,153)(55,152)(56,151)(57,150)(58,149)(59,148)(60,147)(61,146)(62,145)(63,144)(64,143)(65,142)(66,141)(67,140)(68,139)(69,138)(70,137)(71,136)(72,135)(73,134)(74,133)(75,132)(76,131)(77,130)(78,129)(79,128)(80,127)(81,126)(82,125)(83,124)(84,123)(85,122)(86,121)(87,120)(88,119)(89,118)(90,117)(91,116)(92,115)(93,114)(94,113)(95,112)(96,111)(97,110)(98,109)(99,108)(100,107)(101,106)(102,105)(103,104)

Conjugacy classes & character table

7428 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29694, 5);

C3×D4949 #44445940