C₁₁×#23470 #14600663

order	2816
nilpotency class	3
isoclinism	isoclinic class of #23444
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₁×#23470

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₁
prime radical	C₂⁴×C₁₁	C₂⁴
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

1178 conjugacy classes of subgroups; only the 334 normal subgroups are shown.

normal subgroups only

This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 334 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) = 51
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 4 generators on 51 points:

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

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 16458);