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C₂×#62957 #10586302

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

Aliases

Subgroups

35322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493498);