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C₂×#24352 #6445515

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

Aliases

Subgroups

3874 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6352711);