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C₂×#61648 #10577252

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

Aliases

Subgroups

8038 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)(13,20)(14,15)(17,24)(18,22)(21,23)(25,26);(3,5)(4,7)(6,10)(8,9)(11,12,16,19)(13,17,21,26)(14,22,15,18)(20,24,23,25);(11,13)(12,17)(14,20)(15,23)(16,21)(18,25)(19,26)(22,24);(5,10)(7,9)(11,14,16,15)(12,18,19,22)(13,20,21,23)(17,25,26,24);(4,8)(7,9)(12,19)(17,26)(18,22)(24,25)

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, 10484448);