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C₂×#14667 #544376

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

Aliases

Subgroups

4794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 451572);