C₁₇×D₁₂ #87985

order	408
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₇×D₁₂
unambiguous semidirect product	C₄⋊(D₃×C₁₇)

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 204

A minimal faithful permutation representation — 2 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(408, 22);