C₂×C₅×D₁₅₇₃ #44538102

order	31460
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×D₁₅₇₃
unambiguous semidirect product	(C₂×C₁₃)⋊(C₅×D₁₂₁)

Splittings

Fitting	C₂×C₅×C₁₃×C₁₂₁ ⋊ C₂
derived, Hall	C₁₃×C₁₂₁ ⋊ C₂²×C₅
Hall	C₅×C₁₃×C₁₂₁ ⋊ C₂²
Hall	C₅×C₁₂₁ ⋊ C₂×D₁₃
Sylow	C₁₂₁ ⋊ C₂×C₅×D₁₃
Hall	C₅×C₁₃ ⋊ C₂×D₁₂₁
Sylow	C₁₃ ⋊ C₂×C₅×D₁₂₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₅₇₃
commutator, cosocle, hypocenter	C₁₃×C₁₂₁	C₂²×C₅
Frattini	C₁₁	C₂×C₅×D₁₄₃
Fitting	C₂×C₅×C₁₃×C₁₂₁	C₂
socle	C₂×C₅×C₁₁×C₁₃	D₁₁
LCS	G ▷ C₁₃×C₁₂₁
UCS	C₁ ◁ C₂×C₅

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 141
transitive degree	μ_t(G) = 15730

A minimal faithful permutation representation — 2 generators on 141 points:

(3,4,5,6,7)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(22,24)(23,27)(25,30)(26,33)(28,36)(29,35)(31,40)(32,43)(34,45)(37,49)(38,48)(39,47)(41,54)(42,57)(44,59)(46,61)(50,66)(51,65)(52,64)(53,63)(55,72)(56,75)(58,77)(60,79)(62,81)(67,87)(68,86)(69,85)(70,84)(71,83)(73,74)(76,94)(78,96)(80,98)(82,100)(88,101)(89,105)(90,104)(91,103)(92,102)(93,110)(95,112)(97,114)(99,116)(106,117)(107,120)(108,119)(109,118)(111,124)(113,126)(115,128)(121,129)(122,131)(123,130)(125,134)(127,136)(132,137)(133,138)(135,140)(139,141);(1,2)(8,9,11,13,15,17,19,20,18,16,14,12,10)(21,35,64,104,131,141,133,108,70,39,24,27,48,85,120,137,135,123,91,53,30,33,36,65,105,129,127,125,109,71,40,43,45,49,86,117,115,113,111,92,54,57,59,61,66,101,99,97,95,93,72,75,77,79,81,87,82,80,78,76,74,73,94,96,98,100,67,62,60,58,56,55,110,112,114,116,88,50,46,44,42,41,102,124,126,128,106,68,37,34,32,31,83,118,134,136,121,89,51,28,26,25,63,103,130,140,132,107,69,38,23,22,47,84,119,138,139,122,90,52,29)

Conjugacy classes & character table

7880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 42);

C2×C5×D1573 #44538102