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C₂×#63049 #10586368

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

Aliases

Subgroups

34656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493564);