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C₂×#60580 #10575114

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

Aliases

Subgroups

7748 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10482310);