C₁₁×#11478 #14588671

order	2816
nilpotency class	4
isoclinism	isoclinic class of #353
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₁×#11478

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#99
commutator	C₂×C₄	C₂²×C₈×C₁₁
Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×#99
prime radical	C₂³×C₁₁	C₂×C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₄×Q₈×C₁₁ ◁ G

428 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 134 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) = 35
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4466);