C₁₀₇×#1336 #28332019

order	13696
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₀₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₀₇×#1336

Subgroups

	subgroup	G/H
center	C₄×C₁₀₇	#102
commutator	C₈	C₂×C₈×C₁₀₇
Frattini, cosocle	C₄×C₈	C₂²×C₁₀₇
socle	C₂×C₁₀₇	D₄⋊C₈
prime radical	#135×C₁₀₇	C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₀₇ ◁ C₂×C₈×C₁₀₇ ◁ C₄×C₈×C₁₀₇ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 123
transitive degree	μ_t(G) = 1712

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

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₁₀₇×#1336, C₁₀₇×#11604, C₁₀₇×#11669, …
maximal normal subgroup of	C₂×C₁₀₇×#1336, C₁₀₇×#11604, C₁₀₇×#11669, …
maximal quotient of	C₁₀₇×#7070, C₁₀₇×#7071, C₁₀₇×#7072, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 68);

C107×#1336 #28332019