C₁₁×#7505 #14584698

order	2816
nilpotency class	5
isoclinism	isoclinic class of #1412
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#7505

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#354
commutator	C₄²	C₄²×C₁₁
Frattini, cosocle	C₂×C₄⋊Q₈	C₂²×C₁₁
prime radical	C₂³×C₁₁	#99
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×C₄⋊Q₈ ◁ G

260 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 47
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 2 generators on 47 points:

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

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 493);