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C₂×#3239 #60850

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

Aliases

Subgroups

1009 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53838);