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C₂×#11191 #357958

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

Aliases

Subgroups

2750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

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, 265154);