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C₂×#33760 #7623292

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

Aliases

Subgroups

1872 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530488);