C₁₃×#9970 #15696309

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9914
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#9970

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₁₃×#2656	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

772 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 138 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) = 41
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 41 points:

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

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, 2958);