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C₂×#3507 #62777

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

Aliases

Subgroups

3565 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 55765);