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C₂×#52009 #7708072

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

Aliases

Subgroups

8836 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7615268);