C₅×#3624 #10621745

order	680
isoclinism	isoclinic class of #595
automorphism	?
homology	Abelianization (H₁) = C₅×C₈ · Schur multiplier (H₂) = C₁

Aliases

derived, Sylow	C₁₇ ⋊ C₅×C₈
Hall	C₅×C₁₇ ⋊ C₈

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 680

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4,5)(7,8,9,11)(10,13,14,18)(12,17,15,16)(19,21,22,20)(23,24,25,27,26,28,29,30);(6,7,10,15,11,16,20,22,18,13,19,21,17,8,12,14,9)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(680, 5);