C₁₃×#13458 #15699797

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13371
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#13458

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#476
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	AGL(1,ℤ/8)
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

324 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 49
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 49 points:

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

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, 6446);