C₅×#75981 #14327214

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

Aliases

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

1136 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)(6,7,8)(17,19,20,24)(18,22,21,23);(7,8)(13,14,15,16);(7,8)(17,18,20,21)(19,23,24,22);(9,10,11,12)(14,16)(18,21)(22,23)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 52912);