C₁₀₁×#2988 #27168342

order	12928
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈×C₁₀₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₀₁×#2988

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₀₁	C₂⁴
commutator	C₂	C₂³×C₈×C₁₀₁
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₁
socle	C₂²×C₁₀₁	C₂³×C₄
prime radical	C₂×#41×C₁₀₁	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₁ ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 117
transitive degree	μ_t(G) = 6464

A minimal faithful permutation representation — 4 generators on 117 points:

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

Conjugacy classes & character table

6868 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#8839, C₁₀₁×#8840, C₁₀₁×#8953, …
maximal normal subgroup of	C₁₀₁×#8839, C₁₀₁×#8840, C₁₀₁×#8953, …
maximal quotient of	C₁₀₁×#20543, C₁₀₁×#20555, C₁₀₁×#20569, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 1720);

C101×#2988 #27168342