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C₂×#15594 #609178

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

Aliases

Subgroups

4562 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 516374);