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C₂×#48565 #7703750

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

Aliases

Subgroups

7100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7610946);