C₂²×C₁₁×#543 #14639863

order	2816
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₁ · Schur multiplier (H₂) = C₂¹³

Aliases

direct product

C₂²×C₁₁×#543

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₁
prime radical	C₂⁶×C₁₁	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₁ ◁ G

9310 conjugacy classes of subgroups; only the 6366 normal subgroups are shown.

normal subgroups only

This group has 9310 conjugacy classes of subgroups — too many to draw. Only its 6366 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) = 31
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 6 generators on 31 points:

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

Conjugacy classes & character table

968 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 55658);