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C₂×#18750 #6348663

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

Aliases

Subgroups

3402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6255859);