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C₂×#15579 #609161

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

Aliases

Subgroups

4410 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

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, 516357);