C₃×D₄₃₆₁ #39908576

order	26166
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₄₃₆₁
unambiguous semidirect product	C₈₉⋊(C₃×D₄₉)

Splittings

Fitting, Hall	C₃×C₄₉×C₈₉ ⋊ C₂
derived, Hall	C₄₉×C₈₉ ⋊ C₂×C₃
Hall	C₃×C₈₉ ⋊ D₄₉
Hall	C₃×C₄₉ ⋊ D₈₉
Sylow	C₈₉ ⋊ C₃×D₄₉
Sylow	C₄₉ ⋊ C₃×D₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₄₃₆₁
commutator, cosocle, hypocenter	C₄₉×C₈₉	C₂×C₃
Frattini	C₇	C₃×D₆₂₃
Fitting	C₃×C₄₉×C₈₉	C₂
socle	C₃×C₇×C₈₉	D₇
LCS	G ▷ C₄₉×C₈₉
UCS	C₁ ◁ C₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 141
transitive degree	μ_t(G) = 13083

A minimal faithful permutation representation — 2 generators on 141 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);(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)(54,141)(55,140)(56,139)(57,138)(58,137)(59,136)(60,135)(61,134)(62,133)(63,132)(64,131)(65,130)(66,129)(67,128)(68,127)(69,126)(70,125)(71,124)(72,123)(73,122)(74,121)(75,120)(76,119)(77,118)(78,117)(79,116)(80,115)(81,114)(82,113)(83,112)(84,111)(85,110)(86,109)(87,108)(88,107)(89,106)(90,105)(91,104)(92,103)(93,102)(94,101)(95,100)(96,99)(97,98)

Conjugacy classes & character table

6546 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26166, 5);

C3×D4361 #39908576