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C₂×#55034 #8102221

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

Aliases

Subgroups

8348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8009417);