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C₂×#2981 #60229

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

Aliases

Subgroups

1115 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53217);