C₁₇×C₃²⋊C₉ #13063377

order	1377
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃×C₉×C₁₇ · Schur multiplier (H₂) = C₃²

Aliases

direct product	C₁₇×C₃²⋊C₉
unambiguous semidirect product	C₃²⋊(C₉×C₁₇)
unambiguous semidirect product	(C₃²×C₁₇)⋊C₉

46 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 459

A minimal faithful permutation representation — 2 generators on 35 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1377, 3);