C₅×C₃⋊(C₃⋊C₃₂) #13083903

order	1440
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₅×C₃₂ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₅×C₃⋊(C₃⋊C₃₂)
unambiguous semidirect product	C₃⋊(C₅×C₃⋊C₃₂)

derived, Sylow	C₃² ⋊ C₅×C₃₂
Hall	C₃²×C₅ ⋊ C₃₂

72 conjugacy classes of subgroups.

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1440

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5)(6,7,8,12,9,13,16,22,10,14,17,23,19,25,28,32,11,15,18,24,20,26,29,33,21,27,30,34,31,35,36,37)(39,40)(42,43);(41,42,43);(38,39,40)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 220);