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C₂×#53422 #8102029

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

Aliases

Subgroups

9176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8009225);