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C₂×#49917 #7705169

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

Aliases

Subgroups

6262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7612365);