C₂×C₈×C₉⋊C₉ #13046869

order	1296
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₈×C₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₈×C₉⋊C₉
unambiguous semidirect product	(C₂×C₈×C₉)⋊C₉

187 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 1296

A minimal faithful permutation representation — 2 generators on 28 points:

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

maximal subgroup of	C₂×C₈×#6900, #97×C₉⋊C₉, #106×C₉⋊C₉, …
maximal normal subgroup of	C₂×C₈×#6900, #97×C₉⋊C₉, #106×C₉⋊C₉, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 587);