C₆₁×#401 #16839295

order	3904
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂³×C₆₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₆₁×#401

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₆₁	C₂³
commutator, Frattini, cosocle	C₂³	C₂³×C₆₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ G

118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 85
transitive degree	μ_t(G) = 3904

A minimal faithful permutation representation — 3 generators on 85 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61)(64,68)(66,69)(71,74)(75,76)(78,79,81,83)(80,84,85,82);(62,63,65,67)(64,69,68,66)(70,71,73,74)(72,76,77,75)(78,79)(80,84)(81,83)(82,85);(62,64)(63,66)(65,68)(67,69)(70,72,73,77)(71,75,74,76)(78,80,81,85)(79,82,83,84)

Conjugacy classes & character table

1342 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#401×#6923, #30609191, #30609273, …
maximal subgroup of	C₂×C₆₁×#401, C₆₁×#2401, C₆₁×#2493, …
maximal normal subgroup of	C₂×C₆₁×#401, C₆₁×#2401, C₆₁×#2493, …
maximal quotient of	C₆₁×#1443, C₆₁×#2104, C₂×C₆₁×#401

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3904, 82);

C61×#401 #16839295