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C₂×#38199 #7635466

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

Aliases

Subgroups

6652 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(12,15)(16,18)(19,20)(21,25)(22,24)(23,26);(4,7)(5,9)(12,15)(13,17)(19,20,22,24)(21,23,26,25);(3,4,6,7)(5,8,9,10)(11,12,14,15)(13,16,17,18)(19,20)(21,23)(22,24)(25,26);(19,21)(20,23)(22,26)(24,25);(3,5)(4,8)(6,9)(7,10)(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, 7542662);