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C₂×#44157 #7668494

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

Aliases

Subgroups

8022 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)(22,24)(23,26);(3,4)(5,7)(6,9)(8,10)(11,12)(13,18)(14,16)(15,17)(19,20)(21,25)(22,24)(23,26);(4,5)(8,9)(11,12,14,16)(13,15,17,18)(19,20,22,24)(21,23,26,25);(3,5,7,4)(6,9,10,8)(11,12)(13,15)(14,16)(17,18)(19,20)(21,23)(22,24)(25,26);(3,6)(4,8)(5,9)(7,10)(11,13)(12,15)(14,17)(16,18)(19,21,22,26)(20,23,24,25)

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, 7575690);