C₁₀₁×#3137 #27168491

order	12928
nilpotency class	3
isoclinism	isoclinic class of #3057
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₁ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₀₁×#3137

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₁
prime radical	C₂×#41×C₁₀₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ #117×C₁₀₁ ◁ G

372 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 125
transitive degree	μ_t(G) = 6464

A minimal faithful permutation representation — 4 generators on 125 points:

(1,2)(3,5)(4,6)(7,8)(9,10,14,17)(11,18,20,19)(12,22,16,13)(15,23,24,21)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125);(1,3,4,7)(2,5,6,8)(9,11,13,21,14,20,22,23)(10,15,16,18,17,24,12,19);(2,6)(5,8)(9,12,13,10,14,16,22,17)(11,19,21,15,20,18,23,24);(11,20)(15,24)(18,19)(21,23)

Conjugacy classes & character table

3232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#26849, C₁₀₁×#26851, C₁₀₁×#26852, …
maximal normal subgroup of	C₁₀₁×#26849, C₁₀₁×#26851, C₁₀₁×#26852, …
maximal quotient of	C₁₀₁×#20763, C₁₀₁×#21087, C₁₀₁×#21088, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 1869);

C101×#3137 #27168491