C₂×C₁₁×#500 #13065997

order	1408
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×C₁₁×#500

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

424 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 264 normal subgroups are shown.

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

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 4 generators on 29 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1891);