C₁₀₁×#3204 #27168558

order	12928
nilpotency class	3
isoclinism	isoclinic class of #3198
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₀₁×#3204

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×#41×C₁₀₁ ◁ G

402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 125 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₁×#12119, C₁₀₁×#12303
maximal normal subgroup of	C₁₀₁×#12119, C₁₀₁×#12303
maximal quotient of	C₁₀₁×#21772, C₁₀₁×#21946, C₁₀₁×#22053, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 1936);

C101×#3204 #27168558