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C₂×#54991 #8102317

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

Aliases

Subgroups

7180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8009513);