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C₂×#18134 #6346374

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

Aliases

Subgroups

4046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6253570);