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C₂×#50887 #7706593

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

Aliases

Subgroups

7582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(7,8,11,13)(9,10,14,12)(15,16,20,23)(17,21,24,29)(18,19,22,28)(25,30,27,26);(7,9,11,14)(8,12,13,10)(17,24)(18,22)(19,28)(21,29);(3,4,5,6)(15,17)(16,21)(18,27)(19,26)(20,24)(22,25)(23,29)(28,30);(7,9)(8,10)(11,14)(12,13)(15,18,20,22)(16,19,23,28)(17,25,24,27)(21,30,29,26);(7,10)(8,9)(11,12)(13,14)(15,19)(16,22)(17,26)(18,23)(20,28)(21,25)(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, 7613789);