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C₂×#36522 #7630210

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

Aliases

Subgroups

6450 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537406);