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C₂×#50850 #7706282

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

Aliases

Subgroups

7626 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7613478);