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C₂×#38354 #7635424

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

Aliases

Subgroups

5812 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7542620);