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C₂×#61378 #10576209

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

Aliases

Subgroups

6614 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)(11,12,15,18)(13,16,20,24)(14,17,22,19)(21,23,26,25);(3,5,7,10)(4,8,6,9)(11,13)(12,16)(14,21)(15,20)(17,23)(18,24)(19,25)(22,26);(12,17)(14,22)(16,23)(18,19)(21,26)(24,25);(3,6,7,4)(5,8,10,9)(12,18)(16,24)(17,19)(23,25);(13,20)(16,24)(21,26)(23,25)

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, 10483405);