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C₂×#42627 #7641109

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

Aliases

Subgroups

6812 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7548305);