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C₂×#29235 #6461177

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

Aliases

Subgroups

2750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6368373);