C₁₁×#2024 #13064862

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

290 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 108 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) = 1408

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 756);