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C₂×#62759 #10586159

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

Aliases

Subgroups

35154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493355);