C₁₁×#9970 #14587163

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9914
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#9970

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₁	#120
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₁₁×#2656	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ 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) = 39
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 2958);