C₁₁×#10110 #14587303

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10104
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#10110

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₁₁×#3253	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

498 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 106 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)(12,13)(14,21)(15,26)(16,19)(17,20)(18,23)(22,25)(24,27)(30,36)(31,38)(33,41)(34,39)(37,40)(42,43);(12,14,17,25)(13,18,20,27)(15,24,16,23)(19,22,26,21)(28,29,32,35)(30,33,37,42)(31,39,38,34)(36,43,40,41);(12,13)(14,22)(15,19)(16,26)(17,20)(18,23)(21,25)(24,27)(28,30)(29,33)(31,40)(32,37)(34,43)(35,42)(36,38)(39,41)

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 3098);