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C₂×#48774 #7704183

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

Aliases

Subgroups

9098 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7611379);