C₁₁₃×#1375 #28386171

order	14464
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁₃×#1375

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁₃	C₄²
commutator	C₄	C₄×C₈×C₁₁₃
Frattini, cosocle	C₂²×C₈	C₂²×C₁₁₃
socle	C₂²×C₁₁₃	#97
prime radical	C₂³×C₁₁₃	M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁₃ ◁ G

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 133
transitive degree	μ_t(G) = 3616

A minimal faithful permutation representation — 2 generators on 133 points:

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

Conjugacy classes & character table

4972 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₁₃×#7109, C₁₁₃×#7116, C₁₁₃×#7117, …
maximal normal subgroup of	C₁₁₃×#7109, C₁₁₃×#7116, C₁₁₃×#7117, …
maximal quotient of	C₁₁₃×#7137, C₁₁₃×#7142, C₁₁₃×#7145, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 107);

C113×#1375 #28386171