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C₂×#28824 #6465782

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

Aliases

Subgroups

1778 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6372978);