C₁₁×#9190 #14586383

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9183
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#9190

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂³×C₁₁	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

436 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 122 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)(13,16,17,18)(20,21,25,29,26,30,24,40)(22,31,35,42,34,46,33,27)(23,36,38,44,39,28,37,43)(32,45,49,41,48,51,47,50);(12,13,14,18,15,17,19,16)(20,22,26,34)(21,27)(23,32,39,48)(24,33,25,35)(28,41)(29,31)(30,42)(36,50)(37,47,38,49)(40,46)(43,51)(44,45);(20,23,26,39)(21,28,30,36)(22,32,34,48)(24,38,25,37)(27,41,42,50)(29,44,40,43)(31,45,46,51)(33,49,35,47)

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 2178);