C₁₁×#10259 #14587452

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10254
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#10259

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂³×C₁₁	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

474 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 43
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 3 generators on 43 points:

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

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 3247);