C₁₁×#11960 #14589153

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11858
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#11960

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₁₁×#3147	C₂
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

392 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 1408

A minimal faithful permutation representation — 3 generators on 51 points:

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

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, 4948);