C₅×#70739 #14280369

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅×C₈ · Schur multiplier (H₂) = C₂×C₄

Aliases

Hall	C₃×C₅ ⋊ C₈×M₁₆
Sylow	C₃ ⋊ C₅×C₈×M₁₆

448 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3,4,5)(6,7,8)(18,21)(22,24);(7,8)(9,10,11,13,12,14,15,16);(7,8)(17,18,19,22,20,21,23,24)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 6067);