C₁₀₁×#2244 #27167598

order	12928
nilpotency class	4
isoclinism	isoclinic class of #2218
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₁ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₀₁×#2244

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₀₁
prime radical	#493×C₁₀₁	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₄²×C₁₀₁ ◁ C₄×C₈×C₁₀₁ ◁ G

152 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)(3,5)(4,6)(7,8)(10,11)(12,13)(14,22)(16,23)(17,20)(18,24)(19,21)(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)(9,10,16,24,14,18,12,11,15,19,13,17,22,20,23,21);(2,6)(5,8)(9,11,12,20,22,24,16,19,15,21,23,18,14,17,13,10)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₁×#12348, C₁₀₁×#12349, C₁₀₁×#12360, …
maximal normal subgroup of	C₁₀₁×#12348, C₁₀₁×#12349, C₁₀₁×#12360, …
maximal quotient of	C₁₀₁×#12890, C₁₀₁×#13149, C₁₀₁×#13206, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 976);

C101×#2244 #27167598