C₅×#70892 #14317113

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₅ ⋊ #2208
Sylow	C₃ ⋊ C₅×#2208

332 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 960

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 42811);