C₃×D₅₃₅₃ #44545817

order	32118
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₅₃₅₃
unambiguous semidirect product	C₅₃⋊(C₃×D₁₀₁)
unambiguous semidirect product	C₁₀₁⋊(C₃×D₅₃)

Splittings

Fitting, socle, Hall	C₃×C₅₃×C₁₀₁ ⋊ C₂
derived, Hall	C₅₃×C₁₀₁ ⋊ C₂×C₃
Hall	C₃×C₁₀₁ ⋊ D₅₃
Hall	C₃×C₅₃ ⋊ D₁₀₁
Sylow	C₁₀₁ ⋊ C₃×D₅₃
Sylow	C₅₃ ⋊ C₃×D₁₀₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₅₃₅₃
commutator, cosocle, hypocenter	C₅₃×C₁₀₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅₃×C₁₀₁	C₂
LCS	G ▷ C₅₃×C₁₀₁
UCS	C₁ ◁ C₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 157
transitive degree	μ_t(G) = 16059

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);(5,56)(6,55)(7,54)(8,53)(9,52)(10,51)(11,50)(12,49)(13,48)(14,47)(15,46)(16,45)(17,44)(18,43)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)(58,157)(59,156)(60,155)(61,154)(62,153)(63,152)(64,151)(65,150)(66,149)(67,148)(68,147)(69,146)(70,145)(71,144)(72,143)(73,142)(74,141)(75,140)(76,139)(77,138)(78,137)(79,136)(80,135)(81,134)(82,133)(83,132)(84,131)(85,130)(86,129)(87,128)(88,127)(89,126)(90,125)(91,124)(92,123)(93,122)(94,121)(95,120)(96,119)(97,118)(98,117)(99,116)(100,115)(101,114)(102,113)(103,112)(104,111)(105,110)(106,109)(107,108)

Conjugacy classes & character table

8034 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32118, 4);

C3×D5353 #44545817