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C₂×#29109 #6461349

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

Aliases

Subgroups

3618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6368545);