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C₂×#45267 #7669983

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

Aliases

Subgroups

11486 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7577179);