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C₂×#29686 #6435067

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

Aliases

Subgroups

4270 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)(13,19)(14,17)(15,18)(16,21)(20,23)(22,25)(24,26);(4,7)(8,10)(11,13)(12,16)(14,20)(15,21)(17,24)(18,19)(22,26)(23,25);(5,9)(8,10)(11,14)(12,17)(13,20)(15,22)(16,23)(18,25)(19,24)(21,26);(3,5,6,9)(4,8,7,10)(14,22)(17,25)(20,26)(23,24)

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6342263);