C₅×D₄⋊(C₃⋊C₁₆) #14277752

order	1920
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₆ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₅×D₄⋊(C₃⋊C₁₆)
unambiguous semidirect product	D₄⋊(C₅×C₃⋊C₁₆)

Hall	C₃×C₅ ⋊ D₄⋊C₁₆
Sylow	C₃ ⋊ C₅×D₄⋊C₁₆

220 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4,5)(6,7,8)(10,13)(11,16)(14,15);(7,8)(9,10)(11,13)(12,15)(14,16)(17,18,19,22,20,23,25,28,21,24,26,29,27,30,31,32)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 3450);