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C₂×#2864 #36634

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

Aliases

Subgroups

1039 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 29622);