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C₂×#23539 #6431953

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

Aliases

Subgroups

5106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339149);