C₁₀₁×#2205 #27167559

order	12928
nilpotency class	4
isoclinism	isoclinic class of #2204
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₀₁×#2205

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₁	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×Q₈	C₂³×C₁₀₁
prime radical	2₋¹⁺⁴×C₁₀₁	C₂²
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₁ ◁ C₂²×C₁₀₁ ◁ C₂×Q₈×C₁₀₁ ◁ G

224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 117
transitive degree	μ_t(G) = 1616

A minimal faithful permutation representation — 3 generators on 117 points:

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

Conjugacy classes & character table

2020 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#13683, C₁₀₁×#13684
maximal normal subgroup of	C₁₀₁×#13683, C₁₀₁×#13684
maximal quotient of	C₁₀₁×#12101, C₁₀₁×#12130, C₁₀₁×#12146, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 937);

C101×#2205 #27167559