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C₂×#24207 #6448795

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

Aliases

Subgroups

3470 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)(10,11)(12,14)(15,16)(17,19)(18,25)(20,23)(21,24)(22,26)(27,30)(28,29);(8,11)(12,13)(15,17,21,23)(16,19,24,20)(18,22,28,30)(25,26,29,27);(4,6)(15,18,21,28)(16,22,24,30)(17,25,23,29)(19,27,20,26);(7,9,10,14)(8,12,11,13)(15,19,21,20)(16,17,24,23)(18,26,28,27)(22,29,30,25)

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, 6355991);