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C₂×#2740 #52175

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

Aliases

Subgroups

1165 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 45163);