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C₂×#47945 #7703761

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

Aliases

Subgroups

8112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7610957);