C₁₁×#8914 #14586107

order	2816
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#8914

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₁	#120
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂²×D₄×C₁₁	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

468 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 134 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) = 39
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 3 generators on 39 points:

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

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, 1902);