C₁₁×#1613 #13064451

order	1408
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₁	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₁
prime radical	C₁₁×#534	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

288 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 352

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 345);