C₃×C₁₇×3₋¹⁺² #13063387

order	1377
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃³×C₁₇ · Schur multiplier (H₂) = C₃²

Aliases

direct product	C₃×C₁₇×3₋¹⁺²
unambiguous semidirect product	C₉⋊(C₃²×C₁₇)
unambiguous semidirect product	(C₉×C₁₇)⋊C₃²

	subgroup	G/H
center, socle	C₃²×C₁₇	C₃²
commutator, Frattini, cosocle	C₃	C₃³×C₁₇
prime radical	C₃³×C₁₇	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₁₇ ◁ G

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 459

A minimal faithful permutation representation — 3 generators on 29 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1377, 13);