C₂×#383⋊C₃ #73169

order	384
isoclinism	isoclinic class of #126⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂×#383⋊C₃
unambiguous semidirect product	(C₂×#383)⋊C₃

Fitting, Sylow	C₂×#383 ⋊ C₃
derived	C₄² ⋊ C₂×C₃×C₄

144 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 5745);