C₁₀₁×#1558 #27166912

order	12928
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₀₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₀₁×#1558

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₁₀₁
Frattini, cosocle	C₄²	C₂³×C₁₀₁
prime radical	C₂³×C₁₀₁	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

228 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:

(1,2,3,6,4,5,7,8)(9,10)(11,17)(12,20)(13,15)(14,18)(16,22)(19,24)(21,23)(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);(2,5)(3,7)(9,11,13,19)(10,14,15,23)(12,21,22,18)(16,24,20,17);(10,15)(14,23)(16,20)(17,24)

Conjugacy classes & character table

2626 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#7483, C₁₀₁×#8498, C₁₀₁×#8524, …
maximal normal subgroup of	C₁₀₁×#7483, C₁₀₁×#8498, C₁₀₁×#8524, …
maximal quotient of	C₁₀₁×#7595, C₁₀₁×#7605, C₁₀₁×#7629, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 290);

C101×#1558 #27166912