C₁₁₃×#1311 #28386107

order	14464
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₈²×C₁₁₃ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₁₃×#1311

Subgroups

	subgroup	G/H
center	C₄×C₈×C₁₁₃	C₂²
commutator	C₂	C₈²×C₁₁₃
Frattini, cosocle	C₄×C₈	C₂²×C₁₁₃
socle, prime radical	C₂²×C₁₁₃	C₄×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₁₁₃ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 137
transitive degree	μ_t(G) = 14464

A minimal faithful permutation representation — 2 generators on 137 points:

(9,10,11,15,12,16,17,22,13,14,18,20,19,21,23,24)(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);(1,2,3,5,4,6,7,8)(10,14)(15,20)(16,21)(22,24)

Conjugacy classes & character table

9040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₁₃×#7053, C₁₁₃×#7074, C₁₁₃×#7075, …
maximal normal subgroup of	C₁₁₃×#7053, C₁₁₃×#7074, C₁₁₃×#7075, …
maximal quotient of	C₁₁₃×#7052, C₁₁₃×#7136, C₁₁₃×#7330, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 43);

C113×#1311 #28386107