C₃×C₁₉×AΣL(1,𝔽₂₇) #17987290

order	4617
nilpotency class	3
isoclinism	isoclinic class of AΣL(1,𝔽₂₇)
automorphism	?
homology	Abelianization (H₁) = C₃³×C₁₉ · Schur multiplier (H₂) = C₃³

Aliases

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

252 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 513

A minimal faithful permutation representation — 3 generators on 31 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 51);