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C₂×#23578 #6432014

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

Aliases

Subgroups

3810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339210);