C₂×C₁₃×#501 #13112219

order	1664
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

C₂×C₁₃×#501

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

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

normal subgroups only

This group has 384 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) = 31
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 4 generators on 31 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31);(3,4,6,8)(5,9,10,7)(12,15)(13,17)(16,18);(3,5,6,10)(4,7,8,9)(12,16)(15,18);(11,12,13,15,14,16,17,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1893);