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C₂×#8712 #189802

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

Aliases

Subgroups

3046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 96998);