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C₂×#35455 #7628823

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

Aliases

Subgroups

9254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536019);