C₁₁×#2065 #13064903

order	1408
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₁
prime radical	C₂²×D₄×C₁₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

284 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 104 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)(12,13,14,15)(20,21,25,27)(22,24,26,23);(16,17)(18,19)(20,22,23,21,25,26,24,27);(13,15)(17,19)(21,22)(23,24)(26,27)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 797);