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C₂×#60484 #10574992

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

Aliases

Subgroups

7942 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)(13,20)(14,19)(15,23)(16,18)(17,21)(22,26)(24,25);(3,5,6,10)(4,7,8,9);(11,13)(12,17)(14,21)(15,24)(16,22)(18,25)(19,26)(20,23);(12,18)(17,25)(19,23)(20,26);(11,14,16,15)(12,19,18,23)(13,21,22,24)(17,26,25,20)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482188);