C₁₃×#13642 #15699981

order	3328
nilpotency class	3
isoclinism	isoclinic class of #1812
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#13642

Subgroups

	subgroup	G/H
center	C₈×C₁₃	#117
commutator	C₂×C₄	C₂²×C₈×C₁₃
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
socle	C₂×C₁₃	#2163
prime radical	C₂³×C₁₃	M₃₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₃ ◁ C₁₃×#346 ◁ G

170 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 45
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 45 points:

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

Conjugacy classes & character table

832 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6630);