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C₂×#33733 #7623224

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

Aliases

Subgroups

1702 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)(12,16)(13,17)(14,20)(18,26)(19,24)(21,25)(22,23);(4,7)(8,10);(11,12,17,23,14,18,21,24,15,19,25,26,20,22,13,16);(3,5,6,9)(4,8,7,10)

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530420);