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C₂×#60520 #10575033

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

Aliases

Subgroups

8162 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)(13,21)(14,18)(15,19)(16,20)(17,22)(23,25)(24,26);(4,7)(8,10)(11,12)(13,17)(14,19)(15,18)(16,20)(21,22)(23,26)(24,25);(3,5,6,9)(4,8,7,10)(11,13)(12,17)(14,22)(15,24)(16,23)(18,25)(19,21)(20,26);(11,14,16,15)(12,18,20,19)(13,22,23,24)(17,25,26,21);(11,14,16,15)(12,19,20,18)(13,22,23,24)(17,21,26,25)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482229);