C₁₁×#7184 #14584377

order	2816
nilpotency class	3
isoclinism	isoclinic class of #1284
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#7184

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#95
commutator	C₂×C₄	C₄×C₈×C₁₁
Frattini, cosocle	C₂³×C₈	C₂²×C₁₁
socle	C₂²×C₁₁	#336
prime radical	C₂⁴×C₁₁	M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

370 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 352

A minimal faithful permutation representation — 2 generators on 35 points:

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

Conjugacy classes & character table

704 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 172);