C₁₁₃×#1561 #28386357

order	14464
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁₃×#1561

Subgroups

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

210 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 129
transitive degree	μ_t(G) = 7232

A minimal faithful permutation representation — 3 generators on 129 points:

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

Conjugacy classes & character table

2938 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₁₃×#8472, C₁₁₃×#8473, C₁₁₃×#8474, …
maximal normal subgroup of	C₁₁₃×#8472, C₁₁₃×#8473, C₁₁₃×#8474, …
maximal quotient of	C₁₁₃×#7598, C₁₁₃×#7602, C₁₁₃×#7632, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 293);