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C₂×#38053 #7635398

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

Aliases

Subgroups

7894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542594);