C₁₃×#13668 #15700007

order	3328
nilpotency class	5
isoclinism	isoclinic class of #13667
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13668

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2184
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
prime radical	C₁₃×#3414	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ C₂×C₁₃×M₃₂ ◁ G

284 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 77
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 77 points:

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

Conjugacy classes & character table

403 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6656);