C₁₃×#12448 #15698787

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12416
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#12448

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₃	#459
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₃
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ C₈²×C₁₃ ◁ G

218 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 3328

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

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

Conjugacy classes & character table

559 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5436);