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C₂×#45456 #7702236

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

Aliases

Subgroups

8972 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7609432);