C₁₁×#8139 #14585332

order	2816
nilpotency class	2
isoclinism	isoclinic class of #7855
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#8139

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×C₄²
commutator	C₂×C₄	C₂×C₄²×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#376
prime radical	C₂³×C₁₁	#117
LCS	G ▷ C₂×C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ G

330 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 174 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)(12,13,14,17,15,16,18,19)(20,21)(22,30,33,43)(23,27)(24,28)(25,29)(26,32,38,46)(31,42,45,50)(34,39)(35,40)(36,41)(37,44,48,51)(47,49);(20,22)(21,26,29,38)(23,31)(24,32)(25,33)(27,37,40,48)(28,30,41,43)(34,44)(35,45)(36,46)(39,42,49,50)(47,51);(13,16)(17,19)(20,23,24,34,25,35,36,47)(21,27,28,39,29,40,41,49)(22,31,32,44,33,45,46,51)(26,37,30,42,38,48,43,50)

Conjugacy classes & character table

704 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1127);