C₁₃×#8533 #15694872

order	3328
nilpotency class	3
isoclinism	isoclinic class of #8528
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#8533

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#379
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

656 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 150 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)(14,15,20,23,18,17,19,22)(16,21,27,29,25,24,26,28)(31,36)(32,39)(33,34)(38,41)(40,42)(43,44);(14,16,18,25)(15,21,17,24)(19,27,20,26)(22,29,23,28)(30,31,35,38)(32,37,40,45)(33,41,34,36)(39,44,42,43);(14,17,18,15)(16,24,25,21)(19,22,20,23)(26,28,27,29)(30,32)(31,37)(33,39)(34,42)(35,40)(36,43)(38,45)(41,44)

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1521);