C₁₁×#10385 #14587578

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10382
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#10385

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#393
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₂⁴×C₁₁	C₂×D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

396 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 90 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)(12,13,15,18)(14,20)(16,19,24,26)(17,25)(21,22)(23,27)(28,29)(30,33)(31,38,40,34)(32,35)(36,41,39,43)(37,42);(12,13)(14,21,23,17)(15,18)(16,19)(20,22,27,25)(24,26)(28,30,32,37)(29,33,35,42)(31,39)(34,43)(36,40)(38,41);(12,14)(13,17)(15,23)(16,25)(18,21)(19,27)(20,26)(22,24)(28,31,32,40)(29,34,35,38)(30,36,37,39)(33,41,42,43)

Conjugacy classes & character table

341 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 3373);