C₁₃×#13517 #15699856

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13313
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#13517

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#466
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	#135
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

250 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 53
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,21)(17,19)(18,20)(22,23,25,30,38,48,52,47,27,32,39,46,26,31,37,29)(24,28,34,41,35,42,51,53,36,44,50,40,33,43,49,45);(14,16,18,17)(15,19,20,21)(22,24)(23,28)(25,34)(26,33)(27,36)(29,45)(30,41)(31,43)(32,44)(35,38)(37,49)(39,50)(40,46)(42,48)(47,53)(51,52);(14,17,18,16)(15,19,20,21)(23,29)(24,33)(25,37)(26,38)(28,40)(30,31)(32,47)(34,50)(35,36)(39,52)(41,44)(42,53)(43,45)(46,48)

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6505);