C₅²×#214 #11925219

order	1200
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅² · Schur multiplier (H₂) = C₅

Aliases

Hall	C₃×C₅² ⋊ SD₁₆
Sylow	C₃ ⋊ C₅²×SD₁₆

160 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 600

A minimal faithful permutation representation — 2 generators on 21 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 429);