C₁₁×#2187 #13065025

order	1408
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₁
prime radical	C₂²×C₁₁×D₈	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂²×C₈×C₁₁ ◁ G

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

normal subgroups only

This group has 256 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) = 31
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 3 generators on 31 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,20,24)(18,21,27,30)(19,28,26,23)(22,31,29,25);(17,21)(18,25)(19,26)(22,23)(24,30)(27,31)(28,29);(13,15)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 919);