C₅×#69750 #14294864

order	1920
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅×C₈ · Schur multiplier (H₂) = C₂×C₄²

Aliases

Hall	C₃×C₅ ⋊ #1744
Sylow	C₃ ⋊ C₅×#1744

592 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 1920

A minimal faithful permutation representation — 3 generators on 28 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20562);