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C₂×#60237 #10574289

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

Aliases

Subgroups

8040 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10481485);