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C₂×#3338 #61229

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

Aliases

Subgroups

971 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)(13,20)(14,18)(15,17)(16,21)(19,23)(22,25)(24,26);(3,5)(4,8)(6,9)(7,10)(11,13)(12,16)(14,21)(15,22)(17,24)(18,20)(19,25)(23,26);(3,6,7,4)(5,9,10,8)(12,17)(15,23)(16,24)(18,19)(20,25)(22,26);(5,10)(8,9)(13,21)(16,20)(22,26)(24,25)

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54217);