C₁₀₇×#1736 #28332419

order	13696
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₀₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₀₇×#1736

Subgroups

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

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 123
transitive degree	μ_t(G) = 6848

A minimal faithful permutation representation — 3 generators on 123 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₇×#10742, C₁₀₇×#10749, C₁₀₇×#10750, …
maximal normal subgroup of	C₁₀₇×#10742, C₁₀₇×#10749, C₁₀₇×#10750, …
maximal quotient of	C₁₀₇×#7873, C₁₀₇×#7876, C₁₀₇×#7879, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 468);

C107×#1736 #28332419