C₁₁×#1673 #13064511

order	1408
nilpotency class	3
isoclinism	isoclinic class of #1665
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₁	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₁₁
prime radical	C₂×D₄×C₁₁	D₄
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)(14,17)(18,19)(20,21,23,26)(22,24,27,25);(12,13,17,19,15,18,14,16);(21,24)(22,27)(25,26)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 405);