C₃²×#3926 #13083900

order	1440
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₃²×C₃₂ · Schur multiplier (H₂) = C₃

Aliases

derived, Sylow	C₅ ⋊ C₃²×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 — 2 generators on 43 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 217);