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C₂×#51858 #7707705

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

Aliases

Subgroups

6434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7614901);