C₅×#87637 #14519950

order	1960
isoclinism	isoclinic class of #5997
automorphism	?
homology	Abelianization (H₁) = C₅×C₈ · Schur multiplier (H₂) = C₇

Aliases

derived, Sylow	C₇² ⋊ C₅×C₈
Hall	C₅×C₇² ⋊ C₈

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 280

A minimal faithful permutation representation — 2 generators on 27 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 47);