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C₂×#33661 #7623066

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

Aliases

Subgroups

1770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530262);