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C₂×#2645 #34618

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

Aliases

Subgroups

915 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 27606);