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C₂×#9428 #200839

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

Aliases

Subgroups

1780 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 108035);