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C₂×#42977 #7641648

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

Aliases

Subgroups

8086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7548844);