C₁₁×#9436 #14586629

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9431
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#9436

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#386
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂³×C₁₁	#123
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

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

normal subgroups only

This group has 400 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) = 1408

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

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

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, 2424);