C₁₃×#32876 #15719215

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

Aliases

direct product

C₁₃×#32876

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2842
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

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

normal subgroups only

This group has 584 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)(14,15,19,23)(16,24,26,20)(17,28,30,21)(18,32,34,22)(25,40,41,35)(27,36,33,39)(29,37,44,42)(31,38,45,43);(14,16,18,33,19,26,34,27)(15,20,22,39,23,24,32,36)(17,29,31,25,30,44,45,41)(21,37,38,35,28,42,43,40);(14,17,18,31,19,30,34,45)(15,21,22,38,23,28,32,43)(16,25,27,29,26,41,33,44)(20,35,36,37,24,40,39,42);(25,41)(29,44)(35,40)(37,42)

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, 25864);