C₁₁₃×#1359 #28386155

order	14464
nilpotency class	4
isoclinism	isoclinic class of #1357
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁₃×#1359

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁₃	#331
commutator	C₄²	C₂×C₄×C₁₁₃
Frattini, cosocle	C₄×C₈	C₂²×C₁₁₃
prime radical	#127×C₁₁₃	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁₃ ◁ C₂×C₄×C₁₁₃ ◁ C₄×C₈×C₁₁₃ ◁ G

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 129
transitive degree	μ_t(G) = 1808

A minimal faithful permutation representation — 2 generators on 129 points:

(1,2,3,8,11,6,10,14,5,9,13,16,4,7,12,15)(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);(2,6)(3,10)(4,11)(7,9)(8,16)(12,13)

Conjugacy classes & character table

2599 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₁₃×#7517, C₁₁₃×#7518, C₁₁₃×#7519, …
maximal normal subgroup of	C₁₁₃×#7517, C₁₁₃×#7518, C₁₁₃×#7519, …
maximal quotient of	C₁₁₃×#7094, C₁₁₃×#7095, C₁₁₃×#7107, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 91);

C113×#1359 #28386155