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C₂×#59850 #7665774

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

Aliases

Subgroups

8258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7572970);