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C₂×#52072 #7708161

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

Aliases

Subgroups

8122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7615357);