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C₂×#45336 #7670032

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7577228);