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C₂×#38085 #7635609

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

Aliases

Subgroups

8490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542805);