C₁₁×#12458 #14589651

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12430
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#12458

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₁	#466
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₈×Q₈×C₁₁ ◁ G

192 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 59
transitive degree	μ_t(G) = 2816

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,19)(14,20,22,27)(15,23,25,18)(17,24,26,21)(28,29,33,37)(30,38,42,54)(31,43,45,58)(32,46,44,36)(34,47,49,40)(35,50,51,39)(41,57,56,53)(48,55,52,59);(28,30,39,55,32,41,45,47,33,42,50,59,44,56,31,40)(29,34,43,53,36,48,51,54,37,49,58,57,46,52,35,38);(12,14,16,22)(13,17,19,26)(15,24,25,21)(18,27,23,20)

Conjugacy classes & character table

539 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5446);