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C₂×#24339 #6445452

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

Aliases

Subgroups

3600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6352648);