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C₂×#2586 #34835

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

Aliases

Subgroups

1091 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27823);