C₁₃×#32877 #15719216

order	3328
nilpotency class	3
isoclinism	isoclinic class of #32875
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#32877

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2842
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

594 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 186 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 — 4 generators on 45 points:

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

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 25865);