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C₂×#19962 #6358336

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

Aliases

Subgroups

1976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6265532);