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C₂×#50873 #7706672

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

Aliases

Subgroups

8022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7613868);