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C₂×#19968 #6358357

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

Aliases

Subgroups

2304 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6265553);