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C₂×#36695 #7633394

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

Aliases

Subgroups

5574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540590);