C₁₁×#10612 #14587805

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10611
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#10612

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#396
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂×C₁₁×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

328 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 43
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 43 points:

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

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 3600);