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C₂×#53000 #8092832

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

Aliases

Subgroups

7754 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8000028);