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C₂×#39431 #7636628

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

Aliases

Subgroups

8394 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7543824);