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C₂×#35463 #7628832

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

Aliases

Subgroups

14862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536028);