C₆₁×#13313 #29516746

order	15616
nilpotency class	4
isoclinism	isoclinic class of #13313
automorphism	?
homology	Abelianization (H₁) = C₂³×C₆₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₆₁×#13313

Subgroups

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

556 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 97
transitive degree	μ_t(G) = 3904

A minimal faithful permutation representation — 3 generators on 97 points:

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

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, 6301);