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C₂×#38928 #7636485

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

Aliases

Subgroups

7046 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)(20,23)(21,25);(4,8)(6,9)(12,15)(13,17)(19,20,22,23)(21,24,25,26);(11,12)(13,16)(14,15)(17,18)(19,20)(21,24)(22,23)(25,26);(3,5)(4,9)(6,8)(7,10)(19,21)(20,24)(22,25)(23,26);(3,6,7,9)(4,5,8,10)(11,13,14,17)(12,16,15,18)

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, 7543681);