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C₂×#63018 #10586337

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

Aliases

Subgroups

35198 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)(13,20)(14,22)(15,17)(16,19)(18,24)(21,25)(23,26);(3,4)(5,8)(6,9)(7,10)(11,13,16,15)(12,17,19,20)(14,21,24,23)(18,25,22,26);(3,5)(4,7)(6,10)(8,9)(11,13,16,15)(12,17,19,20)(14,21,24,23)(18,25,22,26);(11,14)(12,18)(13,21)(15,23)(16,24)(17,25)(19,22)(20,26);(3,5)(4,8)(6,10)(7,9)(11,15,16,13)(12,17,19,20)(14,23,24,21)(18,25,22,26);(3,4)(5,7)(6,9)(8,10)(11,12)(13,17)(14,18)(15,20)(16,19)(21,25)(22,24)(23,26)

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, 10493533);