C₁₃×#7160 #15693499

order	3328
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#7160

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₃	D₈
commutator	C₈	C₄×C₈×C₁₃
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₃
socle	C₂²×C₁₃	#335
prime radical	C₂³×C₁₃	#108
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

210 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 126 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 — 2 generators on 49 points:

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

Conjugacy classes & character table

1144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 148);