C₁₀₇×#1283 #28331966

order	13696
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₀₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₀₇×#1283

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₀₇	C₂²⋊C₄
commutator	C₂²	C₄×C₈×C₁₀₇
Frattini, cosocle	C₂×C₄²	C₂²×C₁₀₇
socle	C₂²×C₁₀₇	#95
prime radical	C₂³×C₁₀₇	C₄²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₇ ◁ C₂×C₄²×C₁₀₇ ◁ G

160 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 6848

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

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

Conjugacy classes & character table

4708 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₀₇×#1283, C₁₀₇×#7932, C₁₀₇×#7933, …
maximal normal subgroup of	C₂×C₁₀₇×#1283, C₁₀₇×#7932, C₁₀₇×#7933, …
maximal quotient of	C₁₀₇×#7016, C₁₀₇×#7022, C₁₀₇×#7023, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 15);