C₁₀₁×#2929 #27168283

order	12928
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₀₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₀₁×#2929

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₀₁	C₂³
commutator	C₂²	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₁
socle	C₂²×C₁₀₁	C₂³×C₄
prime radical	#525×C₁₀₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₀₁ ◁ G

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 121
transitive degree	μ_t(G) = 3232

A minimal faithful permutation representation — 4 generators on 121 points:

(1,2)(3,4)(5,6,8,12,9,11,15,18)(7,10,13,17,14,16,19,20)(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);(2,4);(5,7,8,13,9,14,15,19)(6,10,12,17,11,16,18,20);(6,11)(10,16)(12,18)(17,20)

Conjugacy classes & character table

5656 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#8238, C₁₀₁×#8239, C₁₀₁×#8240, …
maximal normal subgroup of	C₁₀₁×#8238, C₁₀₁×#8239, C₁₀₁×#8240, …
maximal quotient of	C₁₀₁×#17900, C₁₀₁×#17901, C₁₀₁×#17902, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 1661);

C101×#2929 #27168283