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C₂×#38032 #7635679

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

Aliases

Subgroups

8604 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542875);