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C₂×#60272 #10574359

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

Aliases

Subgroups

6678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481555);