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C₂×#35317 #7628600

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

Aliases

Subgroups

13218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535796);