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C₂×#10018 #235423

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

Aliases

Subgroups

1906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

62 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 142619);