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C₂×#49597 #7705257

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

Aliases

Subgroups

6202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

(1,2);(11,12)(13,14)(15,17)(16,18)(19,20)(21,28)(22,23)(24,25)(26,29)(27,33)(30,31)(32,34);(4,7)(5,9)(11,13,15,16)(12,14,17,18)(20,25)(21,29)(23,33)(30,32);(3,4,6,7)(5,8,9,10)(11,14,15,18)(12,16,17,13)(19,21)(20,26)(22,32)(23,31)(24,29)(25,28)(27,30)(33,34);(3,4)(5,8)(6,7)(9,10)(11,14)(12,13)(15,18)(16,17)(19,22,24,27)(20,23,25,33)(21,30,29,32)(26,34,28,31);(3,5)(4,8)(6,9)(7,10)(11,13)(12,14)(15,16)(17,18)(19,23)(20,27)(21,31)(22,25)(24,33)(26,30)(28,32)(29,34)

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, 7612453);