C₉×#1712 #11766433

order	1152
nilpotency class	3
isoclinism	isoclinic class of #1705
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂²×C₈

Aliases

420 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 576

A minimal faithful permutation representation — 3 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 444);