C₁₁×#3151 #13065989

order	1408
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

656 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 224 normal subgroups are shown.

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

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 4 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1883);