C₁₃×#10386 #15696725

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10386
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10386

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#393
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

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

normal subgroups only

This group has 602 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) = 37
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 37 points:

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

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3374);