C₁₃×#12851 #15699190

order	3328
nilpotency class	3
isoclinism	isoclinic class of #1828
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#12851

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#381
commutator	C₂³	C₂²×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#1817
prime radical	C₂⁴×C₁₃	C₂×C₈
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ G

416 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 162 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)(14,15,17,22,18,23,29,36,19,20,28,31,30,32,41,42)(16,24,26,37,27,38,40,45,25,21,33,34,39,35,43,44);(15,20)(17,28)(21,24)(23,32)(26,33)(29,41)(35,38)(40,43);(14,16)(15,21,20,24)(17,26)(18,27)(19,25)(22,34,31,37)(23,35,32,38)(28,33)(29,40)(30,39)(36,44,42,45)(41,43)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5839);