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C₂×#32020 #7507410

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

Aliases

Subgroups

2410 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7414606);