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C₂×#21407 #6372428

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

Aliases

Subgroups

3730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

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, 6279624);