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C₂×#63019 #10586338

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

Aliases

Subgroups

35122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493534);