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C₂×#44124 #7668282

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

Aliases

Subgroups

7236 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)(11,12,15,13)(14,17,18,16)(21,25)(23,26);(3,4,7,5)(6,9,10,8)(11,12)(13,15)(14,17)(16,18)(19,20)(21,26)(22,24)(23,25);(4,5)(8,9)(12,13)(16,17)(19,20,22,24)(21,23,25,26);(3,5,7,4)(6,9,10,8)(11,13,15,12)(14,17,18,16)(19,20)(21,23)(22,24)(25,26);(3,6)(4,8)(5,9)(7,10)(11,14,15,18)(12,16,13,17)(19,21)(20,23)(22,25)(24,26)

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, 7575478);