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C₂×#36453 #7630134

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

Aliases

Subgroups

6786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7537330);