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C₂×#14828 #607786

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

Aliases

Subgroups

4574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 514982);