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C₂×#24166 #6448685

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

Aliases

Subgroups

3686 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6355881);