C₁₀₁×#2104 #27167458

order	12928
nilpotency class	3
isoclinism	isoclinic class of #2104
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₀₁×#2104

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₁	#401
commutator, Frattini, cosocle	C₂⁴	C₂³×C₁₀₁
prime radical	C₂⁴×C₁₀₁	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₁ ◁ C₂⁴×C₁₀₁ ◁ G

178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 117
transitive degree	μ_t(G) = 1616

A minimal faithful permutation representation — 3 generators on 117 points:

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

Conjugacy classes & character table

2323 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₀₁×#2104, C₁₀₁×#23847
maximal normal subgroup of	C₂×C₁₀₁×#2104, C₁₀₁×#23847
maximal quotient of	C₁₀₁×#10690, C₁₀₁×#10691, C₁₀₁×#11318, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 836);

C101×#2104 #27167458