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C₂×#55559 #8099381

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

Aliases

Subgroups

6812 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

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, 8006577);