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C₂×#37154 #7634441

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

Aliases

Subgroups

6958 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

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, 7541637);