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C₂×#63021 #10586340

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

Aliases

Subgroups

35160 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)(13,21)(14,16)(15,18)(17,20)(19,25)(22,26)(23,24);(3,4)(5,8)(6,9)(7,10)(11,13,17,15)(12,18,20,21)(14,22,25,24)(16,23,19,26);(3,5)(4,7)(6,10)(8,9)(11,13,17,15)(12,18,20,21)(14,22,25,24)(16,23,19,26);(11,14)(12,19)(13,22)(15,24)(16,20)(17,25)(18,26)(21,23);(3,5)(4,8)(6,10)(7,9)(11,15,17,13)(12,18,20,21)(14,24,25,22)(16,23,19,26);(3,4)(5,7)(6,9)(8,10)(11,16,17,19)(12,14,20,25)(13,23,15,26)(18,22,21,24)

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, 10493536);