C₁₀₇×#1289 #28331972

order	13696
nilpotency class	3
isoclinism	isoclinic class of #1284
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₀₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₀₇×#1289

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₇	#95
commutator	C₂×C₄	C₄²×C₁₀₇
Frattini, cosocle	C₂³×C₄	C₂²×C₁₀₇
prime radical	C₂⁴×C₁₀₇	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₇ ◁ C₂³×C₄×C₁₀₇ ◁ G

228 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 123
transitive degree	μ_t(G) = 3424

A minimal faithful permutation representation — 2 generators on 123 points:

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

Conjugacy classes & character table

3424 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₇×#7076, C₁₀₇×#7077, C₁₀₇×#7078, …
maximal normal subgroup of	C₁₀₇×#7076, C₁₀₇×#7077, C₁₀₇×#7078, …
maximal quotient of	C₁₀₇×#7020, C₁₀₇×#7024, C₁₀₇×#7035, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 21);