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C₂×#45332 #7670014

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

Aliases

Subgroups

11244 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7577210);