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C₂×#31223 #7503789

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

Aliases

Subgroups

2486 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7410985);