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C₂×#33901 #7623784

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

Aliases

Subgroups

1558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530980);