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C₂×#9496 #201649

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

Aliases

Subgroups

2842 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 108845);