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C₂×#15492 #609066

• 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)(9,13)(10,11)(12,14)(15,16,18,20)(17,19,21,22)(23,24,28,27)(25,30,26,29);(8,10)(12,13)(17,21)(19,22)(23,25,28,26)(24,29,27,30);(7,9,11,14)(8,12,10,13)(15,17)(16,19)(18,21)(20,22)(23,26,28,25)(24,29,27,30);(3,4)(5,6)(7,10,11,8)(9,13,14,12)(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, 516262);