C₂×C₁₃×#396 #13111447

order	1664
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂×C₁₃×#396

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
prime radical	C₂⁵×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

908 conjugacy classes of subgroups; only the 328 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 328 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);(7,8,9,10)(12,14);(4,6)(11,12,13,14);(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1121);