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C₂×#54389 #8102270

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

Aliases

Subgroups

6626 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8009466);