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C₂×#50007 #7705127

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

Aliases

Subgroups

7208 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7612323);