C₁₁×#12885 #14590078

order	2816
nilpotency class	3
isoclinism	isoclinic class of #2031
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12885

Subgroups

	subgroup	G/H
center	C₈×C₁₁	#124
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
socle	C₂×C₁₁	#1832
prime radical	C₂³×C₁₁	#131
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₁ ◁ C₂²×C₈×C₁₁ ◁ G

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

normal subgroups only

This group has 234 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) = 75
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 75 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,23,18,24,41,56,19,25,42,57,16,22,38,53)(14,26,30,58,28,47,62,54,31,45,39,70,29,20,43,46)(15,32,36,65,35,52,68,55,37,50,40,71,34,21,48,51)(27,59,60,73,33,66,67,75,61,44,64,72,63,49,69,74);(12,14,16,29,19,31,18,28)(13,20,22,45,25,47,24,26)(15,33,35,61,37,63,34,27)(17,39,38,62,42,30,41,43)(21,49,32,59,52,66,50,44)(23,54,53,58,57,46,56,70)(36,69,68,60,40,67,48,64)(51,75,65,72,55,74,71,73);(12,15,16,34,19,37,18,35)(13,21,22,50,25,52,24,32)(14,27,28,33,31,61,29,63)(17,40,38,68,42,36,41,48)(20,44,26,49,47,59,45,66)(23,55,53,65,57,51,56,71)(30,64,62,69,39,60,43,67)(46,73,58,75,54,72,70,74)

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5873);