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C₂×#23591 #6432078

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

Aliases

Subgroups

3824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339274);