C₃×#424 #5298

order	192
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) = C₂²×#23900 (order 1024) · Inn(G) = C₂³ · Out(G) = C₂⁴×D₄
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

114 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 857);