C₂×C₁₁×#447 #13065834

order	1408
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁷

Aliases

C₂×C₁₁×#447

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

1048 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.

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

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 4 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1728);