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C₂×#60496 #10574998

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

Aliases

Subgroups

7658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

122 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482194);