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C₂×#16600 #611189

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

Aliases

Subgroups

7042 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(4,6)(8,10)(12,15)(13,17)(20,24)(22,25);(11,12)(13,16)(14,15)(17,18)(19,20,23,24)(21,25,26,22);(7,8)(9,10)(11,12)(13,18)(14,15)(16,17)(19,21,23,26)(20,22,24,25);(3,4)(5,6)(7,8)(9,10)(11,13)(12,16)(14,17)(15,18)(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, 518385);