C₆₁×#13495 #29516928

order	15616
nilpotency class	4
isoclinism	isoclinic class of #13313
automorphism	?
homology	Abelianization (H₁) = C₂³×C₆₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₆₁×#13495

Subgroups

	subgroup	G/H
center, socle	C₂²×C₆₁	#466
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₆₁
prime radical	C₂×#41×C₆₁	D₄
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂²×C₄×C₆₁ ◁ C₂×#131×C₆₁ ◁ G

284 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 101
transitive degree	μ_t(G) = 7808

A minimal faithful permutation representation — 3 generators on 101 points:

(1,2)(3,6)(4,5)(7,8)(9,10,12,17,25,35,39,34,14,19,26,33,13,18,24,16)(11,15,21,28,22,29,38,40,23,31,37,27,20,30,36,32)(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);(2,5)(6,8)(9,11)(10,15)(12,21)(13,20)(14,23)(16,32)(17,28)(18,30)(19,31)(22,25)(24,36)(26,37)(27,33)(29,35)(34,40)(38,39);(1,3,4,7)(2,6,5,8)(10,16)(11,20)(12,24)(13,25)(15,27)(17,18)(19,34)(21,37)(22,23)(26,39)(28,31)(29,40)(30,32)(33,35)

Conjugacy classes & character table

2440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 6483);