C₅×#72134 #14280293

order	1920
isoclinism	isoclinic class of #4656
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂⁶

Aliases

Hall	C₃×C₅ ⋊ #1446
Sylow	C₃ ⋊ C₅×#1446

1472 conjugacy classes of subgroups; only the 458 normal subgroups are shown.

normal subgroups only

This group has 1472 conjugacy classes of subgroups — too many to draw. Only its 458 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 5991);