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C₂×#35447 #7628814

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

Aliases

Subgroups

12486 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536010);