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C₂×#60755 #10575419

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

Aliases

Subgroups

8234 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)(13,17)(14,19)(15,24)(16,20)(18,21)(22,25)(23,26);(3,5)(4,7)(6,10)(8,9)(11,13)(12,17)(14,23)(15,21)(16,22)(18,24)(19,26)(20,25);(5,10)(7,9)(11,13)(12,18)(14,21)(15,23)(16,22)(17,24)(19,25)(20,26);(4,8)(7,9)(11,14,16,15)(12,19,20,24)(13,21,22,23)(17,18,25,26);(12,20)(17,25)(18,26)(19,24)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482615);