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C₂×#33675 #7623076

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

Aliases

Subgroups

1700 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)(12,16)(13,19)(15,22)(17,25)(18,21)(20,26)(23,24);(4,7)(8,10)(11,12,14,16)(13,17,20,24)(15,18,21,22)(19,23,26,25);(11,13)(12,17)(14,20)(15,23)(16,24)(18,26)(19,22)(21,25);(3,5,6,9)(4,8,7,10)(13,20)(17,24)(19,26)(23,25)

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, 7530272);