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C₂×#34074 #7625307

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

Aliases

Subgroups

7570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532503);