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C₂×#45321 #7670023

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

Aliases

Subgroups

11044 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)(11,12,15,16)(13,17,19,20)(14,22,23,18)(21,26,25,24);(3,4,5,6)(12,16)(13,19)(14,23)(24,26);(7,8)(9,10)(11,12)(13,20)(14,18)(15,16)(17,19)(21,26)(22,23)(24,25);(3,4)(5,6)(11,13)(12,17)(14,21)(15,19)(16,20)(18,24)(22,26)(23,25);(11,14,15,23)(12,18,16,22)(13,21,19,25)(17,24,20,26)

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, 7577219);