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C₂×#3516 #62785

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

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, 55773);