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C₂×#36065 #7629560

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

Aliases

Subgroups

7748 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536756);