C₁₁₃×#1709 #28386505

order	14464
nilpotency class	3
isoclinism	isoclinic class of #1705
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁₃ · Schur multiplier (H₂) = C₂×C₈

Aliases

direct product

C₁₁₃×#1709

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁₃	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₁₁₃
prime radical	#493×C₁₁₃	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ C₄²×C₁₁₃ ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 137
transitive degree	μ_t(G) = 7232

A minimal faithful permutation representation — 3 generators on 137 points:

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

Conjugacy classes & character table

4294 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₁₃×#7092, C₁₁₃×#7530, C₁₁₃×#7531, …
maximal normal subgroup of	C₁₁₃×#7092, C₁₁₃×#7530, C₁₁₃×#7531, …
maximal quotient of	C₁₁₃×#8816, C₁₁₃×#9822, C₁₁₃×#9824, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 441);

C113×#1709 #28386505