C₁₉×#10624608 #28352804

order	13851
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₃³×C₁₉ · Schur multiplier (H₂) = C₃³

Aliases

	subgroup	G/H
center, socle	C₃²×C₁₉	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₉
prime radical	C₁₉×C₃²⋊H(3,𝔽₃)	C₃
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₁₉ ◁ C₃⁴×C₁₉ ◁ G

494 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

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

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1539

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,4,7,6,9,3,5,8)(11,13,15)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(2,5,6)(10,11,14,12,15,18,16,13,17);(2,6,5)(4,8,9)

1387 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 168);