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C₂×#2742 #52177

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

Aliases

Subgroups

1111 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 45165);