C₁₃×#9972 #15696311

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

Aliases

direct product

C₁₃×#9972

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

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

normal subgroups only

This group has 632 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)(18,19,22,20)(21,23,25,24)(26,27)(28,31)(29,32)(30,33)(34,37)(35,38)(36,40)(39,41);(19,23)(20,24)(21,25)(26,28,30,35)(27,31,33,38)(29,34,36,41)(32,39,40,37);(15,17)(18,20,22,19)(21,23,25,24)(26,29)(27,32)(28,34)(30,36)(31,37)(33,40)(35,41)(38,39)

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, 2960);