C₁₁×#12455 #14589648

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12433
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₁×#12455

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#466
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₂×D₄×C₁₁	D₈
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₈×D₄×C₁₁ ◁ G

206 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 1408

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

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

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5443);