C₅×#87648 #14519992

order	1960
isoclinism	isoclinic class of #87648
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₇

Aliases

Hall	C₅×C₇² ⋊ Q₈
Sylow	C₇² ⋊ C₅×Q₈

120 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 1960

A minimal faithful permutation representation — 3 generators on 27 points:

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

505 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 89);