C₁₃×#12180 #15698519

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12152
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₃	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₃
prime radical	C₁₃×#537	C₂²
LCS	G ▷ C₂×C₄⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×C₄⋊C₄ ◁ G

472 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 74 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 — 3 generators on 29 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5168);