C₁₁×#8464 #14585657

order	2816
nilpotency class	3
isoclinism	isoclinic class of #8453
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₁×#8464

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₁₁×#3487	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

1002 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 150 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)(14,18,19,16)(15,17)(20,21,25,30,26,31,24,29)(22,32,36,27,35,42,34,41)(23,28,37,43,38,44,39,45)(33,47,48,51,49,46,50,40);(12,14)(13,16)(15,19)(17,18)(20,22)(21,27)(23,33)(24,36)(25,34)(26,35)(28,40)(29,42)(30,32)(31,41)(37,50)(38,49)(39,48)(43,46)(44,51)(45,47);(20,23,26,38)(21,28,31,44)(22,33,35,49)(24,39,25,37)(27,40,41,51)(29,45,30,43)(32,46,42,47)(34,50,36,48)

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, 1452);