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C₂×#60033 #7666040

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

Aliases

Subgroups

7594 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573236);