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C₂×#32623 #7510478

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

Aliases

Subgroups

2442 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7417674);