C₁₃×#2044 #13111102

order	1664
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₃	#120
commutator, Frattini, cosocle	C₂⁴	C₂³×C₁₃
prime radical	C₁₃×#534	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂⁴×C₁₃ ◁ G

382 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 416

A minimal faithful permutation representation — 3 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 776);