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C₂×#9516 #201862

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

Aliases

Subgroups

1846 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 109058);