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C₂×#11829 #481911

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

Aliases

Subgroups

1118 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)(11,12,14,18,15,16,21,23)(13,17,19,24,20,22,25,26);(3,4)(5,8)(6,10)(7,9)(12,16)(17,22);(3,5,7,6)(4,8,9,10)(11,13,15,20)(12,17,16,22)(14,19,21,25)(18,24,23,26)

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 389107);