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C₂×#11903 #482126

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

Aliases

Subgroups

1194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 389322);