C₁₃×#10612 #15696951

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10611
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#10612

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#396
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

328 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 832

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

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

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, 3600);