C₁₃×#12490 #15698829

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12483
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#12490

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₃	#459
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₃
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ C₈²×C₁₃ ◁ G

212 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 3328

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

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

Conjugacy classes & character table

481 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5478);