C₃×#92553 #13093805

order	1500
isoclinism	isoclinic class of C₅⋊(C₅⋊D₅)
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₅³

Aliases

derived, Sylow	C₅³ ⋊ C₃×C₄
Hall	C₃×C₅³ ⋊ C₄

384 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 1500

A minimal faithful permutation representation — 4 generators on 22 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1500, 106);