C₁₁×#2006 #13064844

order	1408
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₁	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

406 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 3 generators on 23 points:

(1,2,3,4,5,6,7,8,9,10,11)(17,21)(18,19)(22,23);(12,13)(14,15)(16,17)(18,23)(19,21)(20,22);(13,15)(16,17)(18,21)(19,23)(20,22)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 738);