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C₂×#30105 #6433421

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

Aliases

Subgroups

3050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6340617);