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C₂×#27588 #6458787

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

Aliases

Subgroups

3482 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)(21,23)(22,24)(25,26);(3,5,6,10)(4,7,8,9)(11,13)(12,15)(14,17)(16,18)(20,23)(24,25);(13,17)(15,18)(20,24)(22,26)(23,25);(4,8)(7,9)(20,23)(24,25)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6365983);