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C₂×#63015 #10586334

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

Aliases

Subgroups

34798 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)(11,12,17,22)(13,20,15,18)(14,16,21,19)(23,26,25,24);(3,4)(5,8)(6,9)(7,10)(11,13,17,15)(12,18,22,20)(14,23,21,25)(16,24,19,26);(3,5)(4,7)(6,10)(8,9)(11,14)(12,19)(13,23)(15,25)(16,22)(17,21)(18,26)(20,24);(11,15,17,13)(12,20,22,18)(14,25,21,23)(16,26,19,24);(3,5)(4,8)(6,10)(7,9)(11,14)(12,16)(13,23)(15,25)(17,21)(18,24)(19,22)(20,26);(3,4)(5,7)(6,9)(8,10)(11,16)(12,21)(13,24)(14,22)(15,26)(17,19)(18,25)(20,23)

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, 10493530);