3₋¹⁺²×C₂₉ #11715979

order	783
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	3₋¹⁺²×C₂₉
unambiguous semidirect product	C₉⋊(C₃×C₂₉)
unambiguous semidirect product	(C₉×C₂₉)⋊C₃

	subgroup	G/H
center, socle	C₃×C₂₉	C₃²
commutator, Frattini, cosocle	C₃	C₃²×C₂₉
prime radical	C₃²×C₂₉	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₂₉ ◁ G

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 261

A minimal faithful permutation representation — 2 generators on 38 points:

(1,2,4,3,6,8,7,5,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38);(2,5,6)(4,8,9)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(783, 4);