C₁₀₁×#1452 #27166806

order	12928
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₀₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₀₁×#1452

Subgroups

	subgroup	G/H
center	C₄²×C₁₀₁	C₂³
commutator	C₂²	C₂×C₄²×C₁₀₁
Frattini, cosocle	C₄²	C₂³×C₁₀₁
socle	C₂²×C₁₀₁	C₂×C₄²
prime radical	C₂³×C₁₀₁	C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₁₀₁ ◁ G

196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 125 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₁×#7147, C₁₀₁×#7197, C₁₀₁×#7198, …
maximal normal subgroup of	C₁₀₁×#7147, C₁₀₁×#7197, C₁₀₁×#7198, …
maximal quotient of	C₁₀₁×#7843, C₁₀₁×#7849, C₁₀₁×#8133, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 184);

C101×#1452 #27166806