C₁₁×#2029 #13064867

order	1408
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₁	#120
commutator, Frattini, cosocle	C₂⁴	C₂³×C₁₁
prime radical	C₂⁵×C₁₁	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂⁴×C₁₁ ◁ G

466 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 176

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)(14,20,21,17)(16,19,23,25)(22,26,27,24);(12,14,15,21)(13,17,18,20)(16,22,23,27)(19,24,25,26);(17,24)(20,26)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 761);