C₁₁×#11539 #14588732

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11521
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#11539

Subgroups

	subgroup	G/H
center	C₄×C₁₁	#410
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₁
socle	C₂×C₁₁	#1467
prime radical	C₂³×C₁₁	C₂×M₁₆
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂×C₈×C₁₁ ◁ C₁₁×#405 ◁ G

270 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 43
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 3 generators on 43 points:

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

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, 4527);