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C₂×#10799 #353482

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

(1,2);(3,4)(5,6)(7,8)(9,17,20,30)(10,14)(11,15)(12,16)(13,19,25,33)(18,29,32,37)(21,26)(22,27)(23,28)(24,31,35,38)(34,36);(7,9)(8,13,16,25)(10,18)(11,19)(12,20)(14,24,27,35)(15,17,28,30)(21,31)(22,32)(23,33)(26,29,36,37)(34,38);(4,6)(7,10,11,21,12,22,23,34)(8,14,15,26,16,27,28,36)(9,18,19,31,20,32,33,38)(13,24,17,29,25,35,30,37)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260678);