C₇×Dic₁₇ #90910

order	476
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₇ · Schur multiplier (H₂) = C₁

Aliases

C₇×Dic₁₇

derived, Sylow	C₁₇ ⋊ C₄×C₇
Hall	C₇×C₁₇ ⋊ C₄

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 476

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(476, 2);