C₁₁×#13660 #14590853

order	2816
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₁×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#13660

Subgroups

	subgroup	G/H
center	C₂×C₁₁×C₁₆	C₂³
commutator	C₂²	C₂²×C₁₁×C₁₆
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₁
socle, prime radical	C₂²×C₁₁	C₂²×C₁₆
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₁₁×C₁₆ ◁ G

158 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 51
transitive degree	μ_t(G) = 2816

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,19)(15,17)(16,18)(20,21,23,28,24,29,35,43,25,22,31,32,37,33,46,47,26,30,36,44,38,45,49,51,39,34,27,40,41,48,42,50);(12,14,16,15)(13,17,18,19);(12,15,16,14)(13,17,18,19)(20,22,23,32,24,33,35,47,25,30,31,44,37,45,46,51,26,34,36,40,38,48,49,50,39,21,27,28,41,29,42,43)

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 6648);