C₄²×C₉⋊C₉ #13046842

order	1296
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃×C₄²×C₉ · Schur multiplier (H₂) = C₃×C₄

Aliases

C₄²×C₉⋊C₉

	subgroup	G/H
center	C₃²×C₄²	C₃²
commutator	C₃	C₃×C₄²×C₉
Frattini, socle, prime radical, cosocle	C₂²×C₃²	C₂²×C₃²
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₄² ◁ G

255 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 1296

A minimal faithful permutation representation — 2 generators on 26 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 560);