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C₂×#9299 #199047

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

Aliases

Subgroups

1798 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 106243);