C₂×C₁₁×#453 #13065852

order	1408
nilpotency class	3
isoclinism	isoclinic class of #453
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂×C₁₁×#453

	subgroup	G/H
center, socle	C₂²×C₁₁	#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

844 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.

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

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 176

A minimal faithful permutation representation — 4 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1746);