C₉×#1889 #11766610

order	1152
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₉ · Schur multiplier (H₂) = C₂⁵

Aliases

867 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 621);