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C₂×#19727 #6357364

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

Aliases

Subgroups

2582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6264560);