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C₂×#37942 #7635175

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

Aliases

Subgroups

6402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542371);