C₁₁×#10516 #14587709

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10512
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#10516

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂³×C₁₁	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

364 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 704

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

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

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, 3504);