C₅×Dic₁₇ #66768

order	340
isoclinism	isoclinic class of D₁₇
automorphism	Aut(G) = C₂×C₄×AGL(1,𝔽₁₇) (order 2176) · Inn(G) = D₁₇ · Out(G) = C₂×C₄×C₈
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

C₅×Dic₁₇

derived, Sylow	C₁₇ ⋊ C₄×C₅
Hall	C₅×C₁₇ ⋊ C₄

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 340

A minimal faithful permutation representation — 2 generators on 26 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(340, 2);