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C₂×#3504 #62807

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

Aliases

Subgroups

3479 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

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, 55795);