C₃×#405 #5279

order	192
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	Aut(G) = C₂²×#23900 (order 1024) · Inn(G) = C₂² · Out(G) = C₂²×D₄²
homology	Abelianization (H₁) = C₂×C₃×C₄² · Schur multiplier (H₂) = C₂×C₄

Aliases

130 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:

(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, 838);