C₅×#68916 #14296709

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₅ · Schur multiplier (H₂) = C₂×C₄

Aliases

Hall	C₃×C₅ ⋊ C₄×#108
Sylow	C₃ ⋊ C₄×C₅×#108

456 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 960

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 22407);