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C₂×#60599 #10575134

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

Aliases

Subgroups

7624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

122 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482330);