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C₂×#34247 #7625488

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

Aliases

Subgroups

7970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 30 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532684);