C₃×D₄₁₄₁ #38733016

order	24846
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₄₁₄₁
unambiguous semidirect product	C₄₁⋊(C₃×D₁₀₁)
unambiguous semidirect product	C₁₀₁⋊(C₃×D₄₁)

Splittings

Fitting, socle, Hall	C₃×C₄₁×C₁₀₁ ⋊ C₂
derived, Hall	C₄₁×C₁₀₁ ⋊ C₂×C₃
Hall	C₃×C₁₀₁ ⋊ D₄₁
Hall	C₃×C₄₁ ⋊ D₁₀₁
Sylow	C₁₀₁ ⋊ C₃×D₄₁
Sylow	C₄₁ ⋊ C₃×D₁₀₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₄₁₄₁
commutator, cosocle, hypocenter	C₄₁×C₁₀₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₄₁×C₁₀₁	C₂
LCS	G ▷ C₄₁×C₁₀₁
UCS	C₁ ◁ C₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 145
transitive degree	μ_t(G) = 12423

A minimal faithful permutation representation — 2 generators on 145 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);(5,44)(6,43)(7,42)(8,41)(9,40)(10,39)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(46,145)(47,144)(48,143)(49,142)(50,141)(51,140)(52,139)(53,138)(54,137)(55,136)(56,135)(57,134)(58,133)(59,132)(60,131)(61,130)(62,129)(63,128)(64,127)(65,126)(66,125)(67,124)(68,123)(69,122)(70,121)(71,120)(72,119)(73,118)(74,117)(75,116)(76,115)(77,114)(78,113)(79,112)(80,111)(81,110)(82,109)(83,108)(84,107)(85,106)(86,105)(87,104)(88,103)(89,102)(90,101)(91,100)(92,99)(93,98)(94,97)(95,96)

Conjugacy classes & character table

6216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24846, 4);

C3×D4141 #38733016