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C₂×#54624 #8103529

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

Aliases

Subgroups

7572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8010725);