C₁₇×Dic₆ #87983

order	408
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×Dic₆
unambiguous semidirect product	C₃⋊(Q₈×C₁₇)

Hall	C₃×C₁₇ ⋊ Q₈
Sylow	C₃ ⋊ Q₈×C₁₇

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 408

A minimal faithful permutation representation — 2 generators on 28 points:

(1,2,3)(4,6,7,11)(5,8,9,10)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28);(2,3)(4,5,7,9)(6,10,11,8)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(408, 20);