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C₂×#44436 #7668277

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

Aliases

Subgroups

6084 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7575473);