C₁₁×#9510 #14586703

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9495
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#9510

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#386
commutator	C₂⁴	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₂²×D₄×C₁₁	C₂×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

522 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 43
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 43 points:

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

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 2498);