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C₂×#14624 #544262

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

Aliases

Subgroups

5130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 451458);