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C₂×#42995 #7641711

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

Aliases

Subgroups

8560 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7548907);