C₂×#525×C₁₀₇ #28334118

order	13696
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₀₇ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂×#525×C₁₀₇

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₀₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₀₇
socle	C₂³×C₁₀₇	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₇ ◁ G

1880 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 121
transitive degree	μ_t(G) = 3424

A minimal faithful permutation representation — 5 generators on 121 points:

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

Conjugacy classes & character table

5992 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₇×#8331, C₁₀₇×#10971, C₁₀₇×#10993, …
maximal normal subgroup of	C₁₀₇×#8331, C₁₀₇×#10971, C₁₀₇×#10993, …
maximal quotient of	C₂×C₁₀₇×#2280, C₂×C₁₀₇×#2290, C₂×C₁₀₇×#2296, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 2167);

C2×#525×C107 #28334118