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C₂×#9942 #234920

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

Aliases

Subgroups

2810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 142116);