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C₂×#61201 #10576359

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

Aliases

Subgroups

7856 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483555);