C₅×#67442 #14277488

order	1920
isoclinism	isoclinic class of #4466
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₈ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃×C₅ ⋊ #1313
Sylow	C₃ ⋊ C₅×#1313

160 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

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

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 1920

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4,5)(6,7,8)(9,10,11,13,12,14,15,16)(18,22,24,25)(19,26)(23,31,32,30)(27,29);(7,8)(17,18,19,23,20,25,27,31,21,24,26,32,28,22,29,30)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 3186);