C₁₃×#10143 #15696482

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10128
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10143

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

434 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 1664

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

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

Conjugacy classes & character table

403 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3131);