C₁₃×#10383 #15696722

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10382
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#10383

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#393
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

404 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 90 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 — 3 generators on 45 points:

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

Conjugacy classes & character table

403 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3371);