C₁₁×#2196 #13065034

order	1408
nilpotency class	4
isoclinism	isoclinic class of #2196
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center, socle	C₂×C₁₁	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×D₄	C₂³×C₁₁
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₁₁ ◁ C₂×D₄×C₁₁ ◁ G

354 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 88

A minimal faithful permutation representation — 3 generators on 19 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,16)(15,17)(18,19);(13,16)(17,19);(14,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 928);