C₆₁×#540 #16839434

order	3904
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₆₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₆₁×#540

Subgroups

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₆₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ G

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 1952

A minimal faithful permutation representation — 4 generators on 77 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)(62,63)(64,68)(65,66)(67,69)(71,74)(72,76);(63,66)(67,68)(70,71,73,74)(72,75,76,77);(62,63)(64,67)(65,66)(68,69)(70,71)(72,75)(73,74)(76,77);(62,64,65,69)(63,67,66,68)(70,72,73,76)(71,75,74,77)

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	#30605515, #30605516, #30605521, …
maximal subgroup of	C₆₁×#3119, C₆₁×#3122, C₆₁×#3126, …
maximal normal subgroup of	C₆₁×#3119, C₆₁×#3122, C₆₁×#3126, …
maximal quotient of	C₆₁×#2314, C₆₁×#2319, C₆₁×#2324, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3904, 221);

C61×#540 #16839434