C₁₃×#3358 #13112416

order	1664
nilpotency class	3
isoclinism	isoclinic class of D₄×D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×Q₈×C₁₃ ◁ G

426 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.

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

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 4 generators on 29 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 2090);