C₅×#66931 #13183005

order	1760
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₅×C₁₁ ⋊ C₂²⋊Q₈
Sylow	C₁₁ ⋊ C₅×C₂²⋊Q₈

148 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 880

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 814);