C₅×#70465 #14296241

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅×C₈ · Schur multiplier (H₂) = C₂²×C₄

Aliases

Hall	C₃×C₅ ⋊ C₈×C₄⋊C₄
Sylow	C₃ ⋊ C₅×C₈×C₄⋊C₄

592 conjugacy classes of subgroups.

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

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21939);