C₅×#74320 #14322291

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₅ · Schur multiplier (H₂) = C₂⁵

Aliases

Hall	C₃×C₅ ⋊ C₄×C₄⋊Q₈
Sylow	C₃ ⋊ C₄×C₅×C₄⋊Q₈

1176 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 1920

A minimal faithful permutation representation — 4 generators on 24 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 47989);