C₁₀₇×#1426 #28332109

order	13696
nilpotency class	5
isoclinism	isoclinic class of #1426
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₀₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₀₇×#1426

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₇	#367
commutator	C₁₆	C₂×C₄×C₁₀₇
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₀₇
prime radical	C₂²×C₁₀₇	SD₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₇ ◁ C₂×C₄×C₁₀₇ ◁ C₂×C₈×C₁₀₇ ◁ C₂×C₁₆×C₁₀₇ ◁ G

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 139
transitive degree	μ_t(G) = 3424

A minimal faithful permutation representation — 2 generators on 139 points:

(2,7,9,20)(3,12)(4,16)(5,17)(8,23)(10,24,27,32)(11,30,28,22)(13,18)(14,26)(15,25)(19,31,29,21)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139);(1,2,8,24,4,10,3,7,17,28,12,21,13,19,23,30,6,9,26,32,18,27,15,20,5,11,25,31,16,29,14,22)

Conjugacy classes & character table

2782 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₀₇×#1426, C₁₀₇×#13638, C₁₀₇×#13657, …
maximal normal subgroup of	C₂×C₁₀₇×#1426, C₁₀₇×#13638, C₁₀₇×#13657, …
maximal quotient of	C₁₀₇×#7463, C₁₀₇×#7474, C₂×C₁₀₇×#1426

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 158);

C107×#1426 #28332109