C₁₁×#1666 #13064504

order	1408
nilpotency class	3
isoclinism	isoclinic class of #1665
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₁	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₁₁
prime radical	C₁₁×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ G

172 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

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

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 27 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,16)(14,18)(17,19)(21,24)(22,26)(25,27);(12,13,14,16,15,17,18,19);(20,21,23,25)(22,27,26,24)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 398);