C₃×C₄⋊Dic₁₇ #11717772

order	816
isoclinism	isoclinic class of Dic₃₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×C₄⋊Dic₁₇
unambiguous semidirect product	C₄⋊(C₃×Dic₁₇)

Hall	C₃×C₁₇ ⋊ C₄⋊C₄
Sylow	C₁₇ ⋊ C₃×C₄⋊C₄

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 816

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(816, 42);