C₃×D₄₈₅₃ #44415148

order	29118
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₄₈₅₃
unambiguous semidirect product	C₂₃⋊(C₃×D₂₁₁)

Splittings

Fitting, socle, Hall	C₃×C₂₃×C₂₁₁ ⋊ C₂
derived, Hall	C₂₃×C₂₁₁ ⋊ C₂×C₃
Hall	C₃×C₂₁₁ ⋊ D₂₃
Sylow	C₂₁₁ ⋊ C₃×D₂₃
Hall	C₃×C₂₃ ⋊ D₂₁₁
Sylow	C₂₃ ⋊ C₃×D₂₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₄₈₅₃
commutator, cosocle, hypocenter	C₂₃×C₂₁₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₂₃×C₂₁₁	C₂
LCS	G ▷ C₂₃×C₂₁₁
UCS	C₁ ◁ C₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 237
transitive degree	μ_t(G) = 14559

A minimal faithful permutation representation — 2 generators on 237 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)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237);(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(28,237)(29,236)(30,235)(31,234)(32,233)(33,232)(34,231)(35,230)(36,229)(37,228)(38,227)(39,226)(40,225)(41,224)(42,223)(43,222)(44,221)(45,220)(46,219)(47,218)(48,217)(49,216)(50,215)(51,214)(52,213)(53,212)(54,211)(55,210)(56,209)(57,208)(58,207)(59,206)(60,205)(61,204)(62,203)(63,202)(64,201)(65,200)(66,199)(67,198)(68,197)(69,196)(70,195)(71,194)(72,193)(73,192)(74,191)(75,190)(76,189)(77,188)(78,187)(79,186)(80,185)(81,184)(82,183)(83,182)(84,181)(85,180)(86,179)(87,178)(88,177)(89,176)(90,175)(91,174)(92,173)(93,172)(94,171)(95,170)(96,169)(97,168)(98,167)(99,166)(100,165)(101,164)(102,163)(103,162)(104,161)(105,160)(106,159)(107,158)(108,157)(109,156)(110,155)(111,154)(112,153)(113,152)(114,151)(115,150)(116,149)(117,148)(118,147)(119,146)(120,145)(121,144)(122,143)(123,142)(124,141)(125,140)(126,139)(127,138)(128,137)(129,136)(130,135)(131,134)(132,133)

Conjugacy classes & character table

7284 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29118, 5);

C3×D4853 #44415148