C₃×D₅₂ #64613

order	312
isoclinism	isoclinic class of Dic₂₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×D₅₂
unambiguous semidirect product	C₄⋊(C₃×D₁₃)

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 156

A minimal faithful permutation representation — 2 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(312, 29);