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C₂×#49724 #7705046

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

Aliases

Subgroups

6760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7612242);