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C₂×#28103 #6459339

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

Aliases

Subgroups

3156 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)(9,13)(10,12)(11,14)(15,16)(17,24)(18,27)(19,23)(20,22)(21,26)(25,29)(28,30);(7,9,10,14)(8,11,12,13)(15,17,18,28,19,26,20,25)(16,21,27,29,23,24,22,30);(4,6)(15,17,19,26)(16,21,23,24)(18,25,20,28)(22,29,27,30);(8,12)(11,13)(15,18,19,20)(16,22,23,27)(17,25,26,28)(21,29,24,30)

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, 6366535);