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C₂×#33627 #7623002

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

Aliases

Subgroups

1740 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530198);