C₂×C₁₃×#461 #13112088

order	1664
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×C₁₃×#461

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

544 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.

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

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 4 generators on 27 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1762);