C₁₇×C₉⋊C₉ #13063378

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

Aliases

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

34 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1377

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)(19,21,24)(22,26,25)(27,28,30,29,31,33,32,34,35);(18,19,22,20,21,25,23,24,26)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1377, 4);