C₁₁×#8935 #14586128

order	2816
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#8935

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#120
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#385
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

412 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 126 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)(13,16)(14,18)(17,19)(20,21,24,28,25,23,32,27)(22,26,30,34,31,29,35,33);(12,13,15,17)(14,19,18,16)(20,22,24,30,25,31,32,35)(21,26,28,34,23,29,27,33);(14,18)(16,19)(20,23)(21,25)(22,29)(24,27)(26,31)(28,32)(30,33)(34,35)

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, 1923);