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C₂×#37667 #7635085

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

Aliases

Subgroups

9114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542281);