C₁₃×#13416 #15699755

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13373
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13416

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#486
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#2041
prime radical	C₁₃×#3150	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

442 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 110 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)(16,19)(17,30)(18,37)(20,29)(21,26)(22,28)(23,33)(24,39)(25,38)(27,36)(31,40)(32,45)(34,43)(35,44)(41,42);(14,16)(15,22)(17,31)(18,25)(19,37)(20,24)(21,29)(23,35)(26,38)(27,34)(28,39)(30,33)(32,43)(36,42)(40,45)(41,44);(14,17,18,32,21,36,39,35)(15,23,24,42,26,43,37,31)(16,27,28,45,29,30,25,44)(19,40,38,34,20,41,22,33)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6404);